%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM013+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:58 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM013+4 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 12:21:11 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(aReductOfIn0_type, type, (
% 0.20/0.42 aReductOfIn0: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(xR_type, type, (
% 0.20/0.42 xR: $i)).
% 0.20/0.42 tff(tptp_fun_W2_12_type, type, (
% 0.20/0.42 tptp_fun_W2_12: $i > $i)).
% 0.20/0.42 tff(tptp_fun_W2_14_type, type, (
% 0.20/0.42 tptp_fun_W2_14: $i > $i)).
% 0.20/0.42 tff(tptp_fun_W0_11_type, type, (
% 0.20/0.42 tptp_fun_W0_11: $i)).
% 0.20/0.42 tff(sdtmndtasgtdt0_type, type, (
% 0.20/0.42 sdtmndtasgtdt0: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(aElement0_type, type, (
% 0.20/0.42 aElement0: $i > $o)).
% 0.20/0.42 tff(aNormalFormOfIn0_type, type, (
% 0.20/0.42 aNormalFormOfIn0: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_W3_10_type, type, (
% 0.20/0.42 tptp_fun_W3_10: ( $i * $i ) > $i)).
% 0.20/0.42 tff(sdtmndtplgtdt0_type, type, (
% 0.20/0.42 sdtmndtplgtdt0: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_W3_13_type, type, (
% 0.20/0.42 tptp_fun_W3_13: $i > $i)).
% 0.20/0.42 tff(iLess0_type, type, (
% 0.20/0.42 iLess0: ( $i * $i ) > $o)).
% 0.20/0.42 tff(aRewritingSystem0_type, type, (
% 0.20/0.42 aRewritingSystem0: $i > $o)).
% 0.20/0.42 tff(isTerminating0_type, type, (
% 0.20/0.42 isTerminating0: $i > $o)).
% 0.20/0.42 tff(tptp_fun_W3_0_type, type, (
% 0.20/0.42 tptp_fun_W3_0: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 (^[W1: $i] : refl((~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))) <=> (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))) <=> ![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (^[W1: $i] : rewrite((~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))) <=> (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))) <=> ![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))) <=> ![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (^[W1: $i] : trans(monotonicity(rewrite(((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)) <=> ((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))), (((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))) <=> ((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))), rewrite(((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))) <=> (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))), (((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))) <=> (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![W1: $i] : ((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))) <=> ![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 ((aElement0(W0!11) & ![W1: $i] : ((aElement0(tptp_fun_W2_12(W1)) & ((W1 = tptp_fun_W2_12(W1)) | ((aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (aElement0(tptp_fun_W3_13(W1)) & aReductOfIn0(tptp_fun_W3_13(W1), W1, xR) & sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1)))) & sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1)))) & sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1)) & ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR)) & aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)) | (~iLess0(W1, W0!11)) | (~aElement0(W1))) & ![W1: $i] : ((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))) <=> (aElement0(W0!11) & ![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (aElement0(tptp_fun_W2_12(W1)) & ((W1 = tptp_fun_W2_12(W1)) | ((aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (aElement0(tptp_fun_W3_13(W1)) & aReductOfIn0(tptp_fun_W3_13(W1), W1, xR) & sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1)))) & sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1)))) & sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1)) & ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR)) & aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))) & ![W1: $i] : ((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 ((~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR)))))) <=> (~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 ((~![W0: $i] : (aElement0(W0) => (![W1: $i] : (aElement0(W1) => (iLess0(W1, W0) => ?[W2: $i] : ((((aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W1, xR)) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2)))) & sdtmndtasgtdt0(W1, xR, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR))) & aNormalFormOfIn0(W2, W1, xR)))) => ?[W1: $i] : (((aElement0(W1) & (((((W0 = W1) | aReductOfIn0(W1, W0, xR)) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) | sdtmndtasgtdt0(W0, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR))) | aNormalFormOfIn0(W1, W0, xR))))) <=> (~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(11,axiom,(~![W0: $i] : (aElement0(W0) => (![W1: $i] : (aElement0(W1) => (iLess0(W1, W0) => ?[W2: $i] : ((((aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W1, xR)) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2)))) & sdtmndtasgtdt0(W1, xR, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR))) & aNormalFormOfIn0(W2, W1, xR)))) => ?[W1: $i] : (((aElement0(W1) & (((((W0 = W1) | aReductOfIn0(W1, W0, xR)) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) | sdtmndtasgtdt0(W0, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR))) | aNormalFormOfIn0(W1, W0, xR))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (~![W0: $i] : ((~aElement0(W0)) | (~![W1: $i] : (?[W2: $i] : (aElement0(W2) & ((W1 = W2) | ((aReductOfIn0(W2, W1, xR) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W1, xR) & sdtmndtplgtdt0(W3, xR, W2))) & sdtmndtplgtdt0(W1, xR, W2))) & sdtmndtasgtdt0(W1, xR, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, xR)) & aNormalFormOfIn0(W2, W1, xR)) | (~iLess0(W1, W0)) | (~aElement0(W1)))) | ?[W1: $i] : (aNormalFormOfIn0(W1, W0, xR) | (aElement0(W1) & (sdtmndtasgtdt0(W0, xR, W1) | (W0 = W1) | sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) & (~?[W2: $i] : aReductOfIn0(W2, W1, xR)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (aElement0(W0!11) & ![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (aElement0(tptp_fun_W2_12(W1)) & ((W1 = tptp_fun_W2_12(W1)) | ((aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (aElement0(tptp_fun_W3_13(W1)) & aReductOfIn0(tptp_fun_W3_13(W1), W1, xR) & sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1)))) & sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1)))) & sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1)) & ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR)) & aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))) & ![W1: $i] : ((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (![W1: $i] : ((~aNormalFormOfIn0(W1, W0!11, xR)) & ((~aElement0(W1)) | ((~sdtmndtasgtdt0(W0!11, xR, W1)) & (~(W0!11 = W1)) & (~sdtmndtplgtdt0(W0!11, xR, W1)) & (~aReductOfIn0(W1, W0!11, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0!11, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))),
% 0.20/0.43 inference(and_elim,[status(thm)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))))) <=> ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 ((~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | (~(aReductOfIn0(W0!11, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W0!11) | (W0!11 = W0!11) | sdtmndtasgtdt0(W0!11, xR, W0!11) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W0!11)))))) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))))) <=> (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | (~(aReductOfIn0(W0!11, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W0!11) | (W0!11 = W0!11) | sdtmndtasgtdt0(W0!11, xR, W0!11) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W0!11)))))) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))))) <=> ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.44 tff(23,plain,
% 0.20/0.44 (((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | (~(aReductOfIn0(W0!11, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W0!11) | (W0!11 = W0!11) | sdtmndtasgtdt0(W0!11, xR, W0!11) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W0!11)))))) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))))) <=> ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | (~(aReductOfIn0(W0!11, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W0!11) | (W0!11 = W0!11) | sdtmndtasgtdt0(W0!11, xR, W0!11) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W0!11)))))) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (~(aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[25, 19])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 ((aNormalFormOfIn0(W0!11, W0!11, xR) | (~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))) | ((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 ((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (aElement0(W0!11)),
% 0.20/0.44 inference(and_elim,[status(thm)],[16])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 ((~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))) | (~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 ((~((~aElement0(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 (aRewritingSystem0(xR) <=> aRewritingSystem0(xR)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(34,axiom,((aRewritingSystem0(xR) & ![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0)))) & isTerminating0(xR)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__587')).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (aRewritingSystem0(xR) & ![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[34])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (aRewritingSystem0(xR)),
% 0.20/0.44 inference(and_elim,[status(thm)],[35])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (aRewritingSystem0(xR)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[36, 33])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : rewrite((![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : refl((![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : rewrite((![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[43, 41])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1)) <=> (~((~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> (~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))) <=> (((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))))), rewrite((((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))) <=> (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))) <=> (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))) <=> ![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((aReductOfIn0(W2, W0, W1) => aElement0(W2)) <=> (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))), (![W2: $i] : (aReductOfIn0(W2, W0, W1) => aElement0(W2)) <=> ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aReductOfIn0(W2, W0, W1) => aElement0(W2))) <=> ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aReductOfIn0(W2, W0, W1) => aElement0(W2))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aReductOfIn0(W2, W0, W1) => aElement0(W2))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.44 tff(50,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aReductOfIn0(W2, W0, W1) => aElement0(W2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mReduct')).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.44 tff(53,plain,(
% 0.20/0.44 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[52])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))) | (~aRewritingSystem0(W1)) | (~aElement0(W0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 39])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0, W1))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[62, 56, 37, 29])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (((~![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))) | (aElement0(tptp_fun_W2_14(W0!11)) | (~aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))) <=> ((~![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))) | aElement0(tptp_fun_W2_14(W0!11)) | (~aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 ((~![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))) | (aElement0(tptp_fun_W2_14(W0!11)) | (~aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 ((~![W2: $i] : (aElement0(W2) | (~aReductOfIn0(W2, W0!11, xR)))) | aElement0(tptp_fun_W2_14(W0!11)) | (~aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (aElement0(tptp_fun_W2_14(W0!11))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[66, 63, 32])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))))))))), rewrite(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))), (((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (^[W0: $i, W1: $i] : refl(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(71,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (^[W0: $i, W1: $i] : rewrite(((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1)) <=> (~((~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> (~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1))) <=> ((~aElement0(W0)) | (~aRewritingSystem0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) <=> ((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))), rewrite((aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)) <=> (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))), ((((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))), rewrite((((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1)))))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))), ((((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))), (![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) <=> ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> (((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))))), rewrite((((~aElement0(W0)) | (~aRewritingSystem0(W1))) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))), (((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))) <=> ![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 (^[W0: $i, W1: $i] : rewrite(((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))) <=> (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))) <=> ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), (((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.45 tff(82,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aRewritingSystem0(W1)) => ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> ((aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2)) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mNFRDef')).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (aNormalFormOfIn0(W2, W0, W1) <=> (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & (~?[W3: $i] : aReductOfIn0(W3, W2, W1)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.45 tff(85,plain,(
% 0.20/0.45 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | ((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1)))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[84])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1))) | ![W2: $i] : (((~aNormalFormOfIn0(W2, W0, W1)) | (aElement0(W2) & sdtmndtasgtdt0(W0, W1, W2) & ![W3: $i] : (~aReductOfIn0(W3, W2, W1)))) & (aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))) | (~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[87, 74])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[88, 69])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | ![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[95, 89, 37, 67])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))) <=> (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[99, 97])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 ((~![W2: $i] : (~((~((~aElement0(W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR) | aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)))) | (~((~aNormalFormOfIn0(W2, tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (~((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[102, 96])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))) | ((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.20/0.47 tff(106,plain,
% 0.20/0.47 ((aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))) | (~aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(107,plain,
% 0.20/0.47 (aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[106, 32])).
% 0.20/0.47 tff(108,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : refl((iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))) <=> (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(109,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))) <=> ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : rewrite((iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))) <=> (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))) <=> ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.47 tff(112,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))) <=> ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite((aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)) <=> (~((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))), ((~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) <=> (~(~((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))), rewrite((~(~((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))) <=> ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))), ((~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) <=> ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))), (![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) <=> ![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))), (((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))) <=> ((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))), rewrite(((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))) <=> (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))), (((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))) <=> (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))), ((iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | ((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))))) <=> (iLess0(W1, W0) | ((~aElement0(W1)) | (~aElement0(W0))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))))), rewrite((iLess0(W1, W0) | ((~aElement0(W1)) | (~aElement0(W0))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1))))))) <=> (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))), ((iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | ((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))))) <=> (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | ((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))))) <=> ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.47 tff(115,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))))) <=> ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) <=> (aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))), (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) <=> ((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)))), rewrite(((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) <=> (sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))), (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) <=> (sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))))), ((((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0)) <=> ((sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) => iLess0(W1, W0)))), rewrite(((sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1))) => iLess0(W1, W0)) <=> ((~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | iLess0(W1, W0))), ((((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0)) <=> ((~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | iLess0(W1, W0)))), (((aElement0(W0) & aElement0(W1)) => (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0))) <=> ((aElement0(W0) & aElement0(W1)) => ((~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | iLess0(W1, W0))))), rewrite(((aElement0(W0) & aElement0(W1)) => ((~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))) | iLess0(W1, W0))) <=> (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))), (((aElement0(W0) & aElement0(W1)) => (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0))) <=> (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0))) <=> ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (((aReductOfIn0(W1, W0, xR) | ?[W2: $i] : ((aElement0(W2) & aReductOfIn0(W2, W0, xR)) & sdtmndtplgtdt0(W2, xR, W1))) | sdtmndtplgtdt0(W0, xR, W1)) => iLess0(W1, W0)))),
% 0.20/0.47 inference(and_elim,[status(thm)],[35])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | ?[W2: $i] : (aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.47 tff(121,plain,(
% 0.20/0.47 ![W0: $i, W1: $i] : (iLess0(W1, W0) | (~(aElement0(W0) & aElement0(W1))) | ((~sdtmndtplgtdt0(W0, xR, W1)) & (~aReductOfIn0(W1, W0, xR)) & ![W2: $i] : (~(aElement0(W2) & aReductOfIn0(W2, W0, xR) & sdtmndtplgtdt0(W2, xR, W1)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[120])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[122, 112])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | ((~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))) <=> ((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | (~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 ((iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))))) <=> ((~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(126,plain,
% 0.20/0.47 ((~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))) <=> (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 ((iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))))) <=> (iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[126])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 ((iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))))) <=> ((~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[127, 125])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | (iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))) <=> ((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | ((~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | (iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))) <=> ((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | (~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[129, 124])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 ((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | (iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 ((~![W0: $i, W1: $i] : (iLess0(W1, W0) | (~aElement0(W1)) | (~aElement0(W0)) | (~(sdtmndtplgtdt0(W0, xR, W1) | aReductOfIn0(W1, W0, xR) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))))) | (~aElement0(W0!11)) | (~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 ((~aElement0(tptp_fun_W2_14(W0!11))) | iLess0(tptp_fun_W2_14(W0!11), W0!11)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[132, 123, 29, 107])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (iLess0(tptp_fun_W2_14(W0!11), W0!11)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[133, 67])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (^[W1: $i] : refl(((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))))) <=> ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))))) <=> ![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (^[W1: $i] : rewrite(((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (aElement0(tptp_fun_W2_12(W1)) & ((W1 = tptp_fun_W2_12(W1)) | ((aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (aElement0(tptp_fun_W3_13(W1)) & aReductOfIn0(tptp_fun_W3_13(W1), W1, xR) & sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1)))) & sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1)))) & sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1)) & ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR)) & aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))) <=> ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (aElement0(tptp_fun_W2_12(W1)) & ((W1 = tptp_fun_W2_12(W1)) | ((aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (aElement0(tptp_fun_W3_13(W1)) & aReductOfIn0(tptp_fun_W3_13(W1), W1, xR) & sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1)))) & sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1)))) & sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1)) & ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR)) & aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR))) <=> ![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (aElement0(tptp_fun_W2_12(W1)) & ((W1 = tptp_fun_W2_12(W1)) | ((aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (aElement0(tptp_fun_W3_13(W1)) & aReductOfIn0(tptp_fun_W3_13(W1), W1, xR) & sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1)))) & sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1)))) & sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1)) & ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR)) & aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))),
% 0.20/0.48 inference(and_elim,[status(thm)],[16])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR))))))))))) <=> ((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR))))) <=> ((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR))))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))) <=> ((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))) <=> ((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR) | (~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 ((~![W1: $i] : ((~aElement0(W1)) | (~iLess0(W1, W0!11)) | (~((~aElement0(tptp_fun_W2_12(W1))) | (~((W1 = tptp_fun_W2_12(W1)) | (~((~(aReductOfIn0(tptp_fun_W2_12(W1), W1, xR) | (~((~aElement0(tptp_fun_W3_13(W1))) | (~aReductOfIn0(tptp_fun_W3_13(W1), W1, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(W1), xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtplgtdt0(W1, xR, tptp_fun_W2_12(W1))))))) | (~sdtmndtasgtdt0(W1, xR, tptp_fun_W2_12(W1))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(W1), xR))) | (~aNormalFormOfIn0(tptp_fun_W2_12(W1), W1, xR)))))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~iLess0(tptp_fun_W2_14(W0!11), W0!11)) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[147, 141, 67, 134])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 (((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 (aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 ((~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))) | (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 ((~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[152, 105])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))) | ![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.20/0.49 tff(156,assumption,(~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))), introduced(assumption)).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 (((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))))) | aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[157, 148])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((tptp_fun_W2_14(W0!11) = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~((~sdtmndtplgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~((~((~aElement0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)))) | (~aReductOfIn0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_13(tptp_fun_W2_14(W0!11)), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), tptp_fun_W2_14(W0!11), xR)))))))) | sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[159, 148])).
% 0.20/0.49 tff(161,plain,
% 0.20/0.49 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.49 tff(163,plain,
% 0.20/0.49 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.49 tff(168,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mTCRDef')).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[169, 165])).
% 0.20/0.49 tff(171,plain,(
% 0.20/0.49 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[170])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.20/0.49 tff(173,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[172, 162])).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 (((sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | ((sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 ((~![W0: $i, W1: $i, W2: $i] : ((sdtmndtasgtdt0(W0, W1, W2) <=> ((W0 = W2) | sdtmndtplgtdt0(W0, W1, W2))) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[179, 173, 37, 29, 67])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 (^[W0: $i, W1: $i, W2: $i] : refl(((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (^[W0: $i, W1: $i, W2: $i] : rewrite(((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[184, 182])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), trans(monotonicity(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)) <=> (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))))), ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) <=> (aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))))))), rewrite((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))))) <=> (aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))), ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) <=> (aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W3: $i] : trans(monotonicity(rewrite((aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)) <=> (~((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))), ((~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))) <=> (~(~((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))), rewrite((~(~((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))) <=> ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))), ((~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))) <=> ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))), (![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))) <=> ![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))), (((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))) <=> ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))), rewrite(((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))) <=> (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))), (((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))) <=> (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))), ((sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))) <=> (sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))), rewrite((sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))) <=> (sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))), ((sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))) <=> (sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))), (((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))) <=> ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))))) & (sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))), rewrite(((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))))) & (sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))) <=> (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))), (((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))) <=> (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))) <=> (((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))))), rewrite((((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2))))))))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))), (((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))) <=> ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 (^[W0: $i, W1: $i, W2: $i] : rewrite(((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (((~sdtmndtplgtdt0(W0, W1, W2)) | (aReductOfIn0(W2, W0, W1) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (((~sdtmndtplgtdt0(W0, W1, W2)) | (aReductOfIn0(W2, W0, W1) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[188])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), rewrite((sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W0, W1)) & sdtmndtplgtdt0(W3, W1, W2)))) <=> (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W0, W1)) & sdtmndtplgtdt0(W3, W1, W2))))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) => (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W0, W1)) & sdtmndtplgtdt0(W3, W1, W2))))) <=> ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W0, W1)) & sdtmndtplgtdt0(W3, W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.50 tff(193,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) => (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : ((aElement0(W3) & aReductOfIn0(W3, W0, W1)) & sdtmndtplgtdt0(W3, W1, W2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mTCDef')).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (sdtmndtplgtdt0(W0, W1, W2) <=> (aReductOfIn0(W2, W0, W1) | ?[W3: $i] : (aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.20/0.50 tff(196,plain,(
% 0.20/0.50 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | (((~sdtmndtplgtdt0(W0, W1, W2)) | (aReductOfIn0(W2, W0, W1) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[195])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))) | ((aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (aElement0(tptp_fun_W3_0(W2, W1, W0)) & aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1) & sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2))) & (sdtmndtplgtdt0(W0, W1, W2) | ((~aReductOfIn0(W2, W0, W1)) & ![W3: $i] : (~(aElement0(W3) & aReductOfIn0(W3, W0, W1) & sdtmndtplgtdt0(W3, W1, W2)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[197, 187])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[198, 185])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 ((~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))))) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))))))) <=> (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 (((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))))) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11)))))))))))) <=> ((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))))) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11)))))))))))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[203, 201])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))))) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[204])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))))) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[205, 200])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 ((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | ((~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))))) | (~(sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 ((~![W0: $i, W1: $i, W2: $i] : ((~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~((~(aReductOfIn0(W2, W0, W1) | (~sdtmndtplgtdt0(W0, W1, W2)) | (~((~aElement0(tptp_fun_W3_0(W2, W1, W0))) | (~aReductOfIn0(tptp_fun_W3_0(W2, W1, W0), W0, W1)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(W2, W1, W0), W1, W2)))))) | (~(sdtmndtplgtdt0(W0, W1, W2) | (~(aReductOfIn0(W2, W0, W1) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0, W1)) | (~sdtmndtplgtdt0(W3, W1, W2)))))))))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 ((~aElement0(tptp_fun_W2_14(W0!11))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[208, 199, 37, 29])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[209, 67])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 (((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~((~aElement0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11))) | (~aReductOfIn0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), W0!11, xR)) | (~sdtmndtplgtdt0(tptp_fun_W3_0(tptp_fun_W2_14(W0!11), xR, W0!11), xR, tptp_fun_W2_14(W0!11))))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | (~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | ((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 ((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 ((aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11)))))) | (~aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[213, 32])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 ((~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))) | (~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 ((~((~(aReductOfIn0(tptp_fun_W2_14(W0!11), W0!11, xR) | (~![W3: $i] : ((~aElement0(W3)) | (~aReductOfIn0(W3, W0!11, xR)) | (~sdtmndtplgtdt0(W3, xR, tptp_fun_W2_14(W0!11))))))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[216, 212])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.20/0.51 tff(220,plain,
% 0.20/0.51 ((~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) | (~((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 ((~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11)) <=> ((W0!11 = tptp_fun_W2_14(W0!11)) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[221, 180])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (^[W0: $i, W1: $i, W2: $i, W3: $i] : refl((sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[223])).
% 0.20/0.51 tff(225,plain,
% 0.20/0.51 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) <=> (~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> (~(~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))))), rewrite((~(~((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))) <=> ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)))), ((~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) <=> ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))))), trans(monotonicity(rewrite((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) <=> (~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))), ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) <=> (~(~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))))), rewrite((~(~((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))) <=> ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))), ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) <=> ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3))))), ((sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))))), rewrite((sdtmndtasgtdt0(W0, W1, W3) | ((~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1))) | ((~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))), ((sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[225])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (^[W0: $i, W1: $i, W2: $i, W3: $i] : trans(monotonicity(trans(monotonicity(rewrite(((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) & aElement0(W3)))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2)) & aElement0(W3)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))), ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) <=> (aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)))), rewrite(((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3)) <=> ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> ((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))))), rewrite(((aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3)) => ((~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))) | sdtmndtasgtdt0(W0, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))), (((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3))) <=> ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[228])).
% 0.20/0.51 tff(230,axiom,(![W0: $i, W1: $i, W2: $i, W3: $i] : ((((aElement0(W0) & aRewritingSystem0(W1)) & aElement0(W2)) & aElement0(W3)) => ((sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3)) => sdtmndtasgtdt0(W0, W1, W3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mTCRTrans')).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.20/0.51 tff(233,plain,(
% 0.20/0.51 ![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~(aElement0(W0) & aRewritingSystem0(W1) & aElement0(W2) & aElement0(W3))) | (~(sdtmndtasgtdt0(W0, W1, W2) & sdtmndtasgtdt0(W2, W1, W3))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[232])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 (![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[234, 224])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 ((sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[237])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) <=> ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[238, 236])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 ((~![W0: $i, W1: $i, W2: $i, W3: $i] : (sdtmndtasgtdt0(W0, W1, W3) | (~aElement0(W3)) | (~aElement0(W2)) | (~aElement0(W0)) | (~aRewritingSystem0(W1)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~sdtmndtasgtdt0(W2, W1, W3)))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | (~aElement0(tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_14(W0!11))) | (~sdtmndtasgtdt0(tptp_fun_W2_14(W0!11), xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[241, 235, 37, 29, 67, 222, 160, 158, 156])).
% 0.20/0.51 tff(243,plain,(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 (((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (^[W2: $i] : rewrite((~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(247,plain,
% 0.20/0.51 (![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))) <=> ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[246])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[247])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) <=> ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[248, 245])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[249])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[250, 244])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | ((~aRewritingSystem0(xR)) | (~aElement0(W0!11)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0!11, xR) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 ((~![W0: $i, W1: $i] : ((~aRewritingSystem0(W1)) | (~aElement0(W0)) | ![W2: $i] : (~((~(aNormalFormOfIn0(W2, W0, W1) | (~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, W1), W2, W1))) | (~((~aNormalFormOfIn0(W2, W0, W1)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0, W1, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, W1))))))))))) | (~aElement0(W0!11)) | (~aRewritingSystem0(xR)) | ![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 (![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[253, 89, 37, 29])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 (((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 ((~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))) <=> (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 (((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.52 tff(258,plain,
% 0.20/0.52 (((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))) <=> ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.52 tff(259,plain,
% 0.20/0.52 ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(260,plain,
% 0.20/0.52 ((~![W2: $i] : (~((~((~aElement0(W2)) | aNormalFormOfIn0(W2, W0!11, xR) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | aReductOfIn0(tptp_fun_W3_10(W2, xR), W2, xR))) | (~((~aNormalFormOfIn0(W2, W0!11, xR)) | (~((~aElement0(W2)) | (~sdtmndtasgtdt0(W0!11, xR, W2)) | (~![W3: $i] : (~aReductOfIn0(W3, W2, xR)))))))))) | (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.52 tff(261,plain,
% 0.20/0.52 (~((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[260, 254])).
% 0.20/0.52 tff(262,plain,
% 0.20/0.52 (((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~((~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))))) | ((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(263,plain,
% 0.20/0.52 ((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.20/0.52 tff(264,plain,
% 0.20/0.52 (((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))) <=> ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(265,plain,
% 0.20/0.52 ((~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))) <=> (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(266,plain,
% 0.20/0.52 (((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))) <=> ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[265])).
% 0.20/0.52 tff(267,plain,
% 0.20/0.52 (((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))) <=> ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[266, 264])).
% 0.20/0.52 tff(268,plain,
% 0.20/0.52 ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(269,plain,
% 0.20/0.52 ((~![W1: $i] : (~(aNormalFormOfIn0(W1, W0!11, xR) | (~((~aElement0(W1)) | (~(aReductOfIn0(W1, W0!11, xR) | sdtmndtplgtdt0(W0!11, xR, W1) | (W0!11 = W1) | sdtmndtasgtdt0(W0!11, xR, W1) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, W1)))))) | aReductOfIn0(tptp_fun_W2_14(W1), W1, xR)))))) | (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.20/0.52 tff(270,plain,
% 0.20/0.52 (~(aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[269, 19])).
% 0.20/0.52 tff(271,plain,
% 0.20/0.52 ((aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR) | (~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | (~(sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | (~![W2: $i] : ((~aElement0(W2)) | (~aReductOfIn0(W2, W0!11, xR)) | (~sdtmndtplgtdt0(W2, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))))) | (W0!11 = tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | sdtmndtplgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))) | aReductOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W2_14(tptp_fun_W2_12(tptp_fun_W2_14(W0!11))), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)))) | (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(272,plain,
% 0.20/0.52 (~aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.20/0.52 tff(273,plain,
% 0.20/0.52 ((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | (~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(274,plain,
% 0.20/0.52 ((~((~aElement0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR))) | aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)))) | aNormalFormOfIn0(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), W0!11, xR)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[273, 158])).
% 0.20/0.52 tff(275,plain,
% 0.20/0.52 (aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR) | (~sdtmndtasgtdt0(W0!11, xR, tptp_fun_W2_12(tptp_fun_W2_14(W0!11))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[274, 272, 263])).
% 0.20/0.52 tff(276,plain,
% 0.20/0.52 (aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[275, 243])).
% 0.20/0.52 tff(277,plain,
% 0.20/0.52 ((~![W3: $i] : (~aReductOfIn0(W3, tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))) | (~aReductOfIn0(tptp_fun_W3_10(tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR), tptp_fun_W2_12(tptp_fun_W2_14(W0!11)), xR))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(278,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[277, 276, 155])).
% 0.20/0.52 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------