%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT387+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:14:37 AM UTC 2025
% Result : Theorem 0.19s 0.46s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT387+4 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 20:50:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.46 % SZS status Theorem
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 tff(sdtlseqdt0_type, type, (
% 0.19/0.46 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(xp_type, type, (
% 0.19/0.46 xp: $i)).
% 0.19/0.46 tff(aElementOf0_type, type, (
% 0.19/0.46 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(xT_type, type, (
% 0.19/0.46 xT: $i)).
% 0.19/0.46 tff(sdtlpdtrp0_type, type, (
% 0.19/0.46 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.46 tff(xf_type, type, (
% 0.19/0.46 xf: $i)).
% 0.19/0.46 tff(aUpperBoundOfIn0_type, type, (
% 0.19/0.46 aUpperBoundOfIn0: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(xU_type, type, (
% 0.19/0.46 xU: $i)).
% 0.19/0.46 tff(xP_type, type, (
% 0.19/0.46 xP: $i)).
% 0.19/0.46 tff(tptp_fun_W1_15_type, type, (
% 0.19/0.46 tptp_fun_W1_15: $i > $i)).
% 0.19/0.46 tff(aSet0_type, type, (
% 0.19/0.46 aSet0: $i > $o)).
% 0.19/0.46 tff(cS1241_type, type, (
% 0.19/0.46 cS1241: ( $i * $i * $i ) > $i)).
% 0.19/0.46 tff(aElement0_type, type, (
% 0.19/0.46 aElement0: $i > $o)).
% 0.19/0.46 tff(szRzazndt0_type, type, (
% 0.19/0.46 szRzazndt0: $i > $i)).
% 0.19/0.46 tff(szDzozmdt0_type, type, (
% 0.19/0.46 szDzozmdt0: $i > $i)).
% 0.19/0.46 tff(isMonotone0_type, type, (
% 0.19/0.46 isMonotone0: $i > $o)).
% 0.19/0.46 tff(aFunction0_type, type, (
% 0.19/0.46 aFunction0: $i > $o)).
% 0.19/0.46 tff(aCompleteLattice0_type, type, (
% 0.19/0.46 aCompleteLattice0: $i > $o)).
% 0.19/0.46 tff(aSupremumOfIn0_type, type, (
% 0.19/0.46 aSupremumOfIn0: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(aInfimumOfIn0_type, type, (
% 0.19/0.46 aInfimumOfIn0: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(aLowerBoundOfIn0_type, type, (
% 0.19/0.46 aLowerBoundOfIn0: ( $i * $i * $i ) > $o)).
% 0.19/0.46 tff(aSubsetOf0_type, type, (
% 0.19/0.46 aSubsetOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(isOn0_type, type, (
% 0.19/0.46 isOn0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(tptp_fun_W2_9_type, type, (
% 0.19/0.46 tptp_fun_W2_9: $i > $i)).
% 0.19/0.46 tff(tptp_fun_W1_10_type, type, (
% 0.19/0.46 tptp_fun_W1_10: $i > $i)).
% 0.19/0.46 tff(tptp_fun_W1_16_type, type, (
% 0.19/0.46 tptp_fun_W1_16: $i > $i)).
% 0.19/0.46 tff(tptp_fun_W0_17_type, type, (
% 0.19/0.46 tptp_fun_W0_17: $i)).
% 0.19/0.46 tff(xS_type, type, (
% 0.19/0.46 xS: $i)).
% 0.19/0.46 tff(tptp_fun_W0_18_type, type, (
% 0.19/0.46 tptp_fun_W0_18: $i)).
% 0.19/0.46 tff(aFixedPointOf0_type, type, (
% 0.19/0.46 aFixedPointOf0: ( $i * $i ) > $o)).
% 0.19/0.46 tff(cS1142_type, type, (
% 0.19/0.46 cS1142: $i > $i)).
% 0.19/0.46 tff(1,plain,
% 0.19/0.46 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(2,plain,
% 0.19/0.47 (![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.47 tff(3,plain,
% 0.19/0.47 (^[W0: $i] : refl((~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(4,plain,
% 0.19/0.47 (![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.47 tff(5,plain,
% 0.19/0.47 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.47 tff(7,plain,
% 0.19/0.47 (![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) <=> ((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))), trans(monotonicity(rewrite(((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))) <=> (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))), ((aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) <=> (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))), rewrite((aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))) <=> (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))), ((aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) <=> (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))), ((((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))) <=> (((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))), rewrite((((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) <=> (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))), ((((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))) <=> (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 (^[W0: $i] : rewrite((((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | aElementOf0(W0, xP))) <=> (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(11,plain,
% 0.19/0.47 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | aElementOf0(W0, xP))) <=> ![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP))) <=> ![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(13,plain,
% 0.19/0.47 (^[W0: $i] : rewrite(((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP))) <=> (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 (![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP))) <=> ![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.48 tff(15,axiom,((aSet0(xP) & ![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))) & (xP = cS1241(xU, xf, xT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1244')).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 (aSet0(xP) & ![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[15])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[16])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.19/0.48 tff(20,plain,(
% 0.19/0.48 ![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | aElementOf0(W0, xP)))),
% 0.19/0.48 inference(skolemize,[status(sab)],[19])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & (aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, xU)) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[20, 11])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[21, 9])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (![W0: $i] : (~((~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[22, 7])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 (![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[23, 2])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 ((~((~(aElementOf0(xp, xP) | (~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~(aUpperBoundOfIn0(xp, xT, xU) | (~aElementOf0(tptp_fun_W1_15(xp), xT)) | sdtlseqdt0(tptp_fun_W1_15(xp), xp))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))))))))) <=> (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(27,plain,
% 0.19/0.48 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(xp, xP) | (~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~(aUpperBoundOfIn0(xp, xT, xU) | (~aElementOf0(tptp_fun_W1_15(xp), xT)) | sdtlseqdt0(tptp_fun_W1_15(xp), xp))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp)))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(xp, xP) | (~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~(aUpperBoundOfIn0(xp, xT, xU) | (~aElementOf0(tptp_fun_W1_15(xp), xT)) | sdtlseqdt0(tptp_fun_W1_15(xp), xp))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp)))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[27, 25])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(xp, xP) | (~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~(aUpperBoundOfIn0(xp, xT, xU) | (~aElementOf0(tptp_fun_W1_15(xp), xT)) | sdtlseqdt0(tptp_fun_W1_15(xp), xp))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp)))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(30,plain,
% 0.19/0.48 ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (~((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[30, 24])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (((~((~aElementOf0(xp, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | aElementOf0(xp, xP) | (~(aUpperBoundOfIn0(xp, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(xp), xp) | (~aElementOf0(tptp_fun_W1_15(xp), xT)))))) | (~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))))))) | ((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 ((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 ((szDzozmdt0(xf) = szRzazndt0(xf)) <=> (szDzozmdt0(xf) = szRzazndt0(xf))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(35,axiom,((((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))) & (szRzazndt0(xf) = xU)) & isOn0(xf, xU)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1123')).
% 0.19/0.49 tff(36,plain,
% 0.19/0.49 (((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))) & (szRzazndt0(xf) = xU)),
% 0.19/0.49 inference(and_elim,[status(thm)],[35])).
% 0.19/0.49 tff(37,plain,
% 0.19/0.49 ((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))),
% 0.19/0.49 inference(and_elim,[status(thm)],[36])).
% 0.19/0.49 tff(38,plain,
% 0.19/0.49 (szDzozmdt0(xf) = szRzazndt0(xf)),
% 0.19/0.49 inference(and_elim,[status(thm)],[37])).
% 0.19/0.49 tff(39,plain,
% 0.19/0.49 (szDzozmdt0(xf) = szRzazndt0(xf)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.49 tff(40,plain,
% 0.19/0.49 (szRzazndt0(xf) = szDzozmdt0(xf)),
% 0.19/0.49 inference(symmetry,[status(thm)],[39])).
% 0.19/0.49 tff(41,plain,
% 0.19/0.49 (aElementOf0(xp, szRzazndt0(xf)) <=> aElementOf0(xp, szDzozmdt0(xf))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.49 tff(42,plain,
% 0.19/0.49 (aElementOf0(xp, szDzozmdt0(xf)) <=> aElementOf0(xp, szRzazndt0(xf))),
% 0.19/0.49 inference(symmetry,[status(thm)],[41])).
% 0.19/0.49 tff(43,plain,
% 0.19/0.49 ((szRzazndt0(xf) = xU) <=> (szRzazndt0(xf) = xU)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(44,plain,
% 0.19/0.49 (szRzazndt0(xf) = xU),
% 0.19/0.49 inference(and_elim,[status(thm)],[36])).
% 0.19/0.49 tff(45,plain,
% 0.19/0.49 (szRzazndt0(xf) = xU),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.49 tff(46,plain,
% 0.19/0.49 (xU = szRzazndt0(xf)),
% 0.19/0.49 inference(symmetry,[status(thm)],[45])).
% 0.19/0.49 tff(47,plain,
% 0.19/0.49 (xU = szDzozmdt0(xf)),
% 0.19/0.49 inference(transitivity,[status(thm)],[46, 40])).
% 0.19/0.49 tff(48,plain,
% 0.19/0.49 (aElementOf0(xp, xU) <=> aElementOf0(xp, szDzozmdt0(xf))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.49 tff(49,plain,
% 0.19/0.49 (aElementOf0(xp, xU) <=> aElementOf0(xp, xU)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(50,axiom,(((((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)) & ![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))) & aInfimumOfIn0(xp, xP, xU)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1261')).
% 0.19/0.49 tff(51,plain,
% 0.19/0.49 ((((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)) & ![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))),
% 0.19/0.49 inference(and_elim,[status(thm)],[50])).
% 0.19/0.49 tff(52,plain,
% 0.19/0.49 (((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)),
% 0.19/0.49 inference(and_elim,[status(thm)],[51])).
% 0.19/0.49 tff(53,plain,
% 0.19/0.49 ((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))),
% 0.19/0.49 inference(and_elim,[status(thm)],[52])).
% 0.19/0.49 tff(54,plain,
% 0.19/0.49 (aElementOf0(xp, xU) & aElementOf0(xp, xU)),
% 0.19/0.49 inference(and_elim,[status(thm)],[53])).
% 0.19/0.49 tff(55,plain,
% 0.19/0.49 (aElementOf0(xp, xU)),
% 0.19/0.49 inference(and_elim,[status(thm)],[54])).
% 0.19/0.49 tff(56,plain,
% 0.19/0.49 (aElementOf0(xp, xU)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[55, 49])).
% 0.19/0.49 tff(57,plain,
% 0.19/0.49 (aElementOf0(xp, szDzozmdt0(xf))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[56, 48])).
% 0.19/0.49 tff(58,plain,
% 0.19/0.49 (aElementOf0(xp, szRzazndt0(xf))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[57, 42])).
% 0.19/0.49 tff(59,plain,
% 0.19/0.49 (aSet0(szRzazndt0(xf)) <=> aSet0(xU)),
% 0.19/0.49 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.49 tff(60,plain,
% 0.19/0.49 (aSet0(xU) <=> aSet0(szRzazndt0(xf))),
% 0.19/0.49 inference(symmetry,[status(thm)],[59])).
% 0.19/0.49 tff(61,plain,
% 0.19/0.49 (aSet0(xU) <=> aSet0(xU)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(62,plain,
% 0.19/0.49 (((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)),
% 0.19/0.49 inference(and_elim,[status(thm)],[37])).
% 0.19/0.49 tff(63,plain,
% 0.19/0.49 ((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))),
% 0.19/0.49 inference(and_elim,[status(thm)],[62])).
% 0.19/0.49 tff(64,plain,
% 0.19/0.49 (((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)),
% 0.19/0.49 inference(and_elim,[status(thm)],[63])).
% 0.19/0.49 tff(65,plain,
% 0.19/0.49 ((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)),
% 0.19/0.49 inference(and_elim,[status(thm)],[64])).
% 0.19/0.49 tff(66,plain,
% 0.19/0.49 (aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))),
% 0.19/0.49 inference(and_elim,[status(thm)],[65])).
% 0.19/0.49 tff(67,plain,
% 0.19/0.49 (aSet0(xU)),
% 0.19/0.49 inference(and_elim,[status(thm)],[66])).
% 0.19/0.49 tff(68,plain,
% 0.19/0.49 (aSet0(xU)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[67, 61])).
% 0.19/0.49 tff(69,plain,
% 0.19/0.49 (aSet0(szRzazndt0(xf))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[68, 60])).
% 0.19/0.49 tff(70,plain,
% 0.19/0.49 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(71,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.49 tff(72,plain,
% 0.19/0.49 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(73,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.49 tff(74,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.49 tff(75,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(76,plain,
% 0.19/0.49 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(77,plain,
% 0.19/0.49 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.49 tff(78,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.19/0.49 tff(79,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.49 tff(80,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.19/0.49 tff(81,plain,(
% 0.19/0.49 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[80])).
% 0.19/0.49 tff(82,plain,
% 0.19/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.19/0.49 tff(83,plain,
% 0.19/0.49 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf)))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(84,plain,
% 0.19/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(85,plain,
% 0.19/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.49 tff(86,plain,
% 0.19/0.49 ((~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.19/0.49 tff(87,plain,
% 0.19/0.49 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[86, 69])).
% 0.19/0.49 tff(88,plain,
% 0.19/0.49 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(89,plain,
% 0.19/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 (aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[90, 87])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (aElement0(xp)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[91, 58])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 (aFunction0(xf) <=> aFunction0(xf)),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 (aFunction0(xf)),
% 0.19/0.49 inference(and_elim,[status(thm)],[64])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 (aFunction0(xf)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.49 tff(96,plain,
% 0.19/0.49 (^[W0: $i] : refl(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(99,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[99, 97])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))) <=> ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), (![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))) <=> ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> (aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))))), rewrite((aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 (![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.49 tff(104,axiom,(![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mImgSort')).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.19/0.49 tff(107,plain,(
% 0.19/0.49 ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[106])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | ((~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | (~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | ((~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | (~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[111, 108, 95])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | (~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | (~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.49 tff(116,plain,
% 0.19/0.49 (aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[115, 57, 112])).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(118,plain,
% 0.19/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 (aElement0(sdtlpdtrp0(xf, xp))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[119, 87, 116])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(122,plain,
% 0.19/0.50 ((~((~(aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))))))))) <=> (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU))))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(123,plain,
% 0.19/0.50 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp))))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)))))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[122])).
% 0.19/0.50 tff(124,plain,
% 0.19/0.50 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp))))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[123, 121])).
% 0.19/0.50 tff(125,plain,
% 0.19/0.50 ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp))))))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(126,plain,
% 0.19/0.50 ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.50 tff(127,plain,
% 0.19/0.50 (~((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)))))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[126, 24])).
% 0.19/0.50 tff(128,plain,
% 0.19/0.50 (((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU))))))) | ((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(129,plain,
% 0.19/0.50 ((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.19/0.50 tff(130,plain,
% 0.19/0.50 (aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)) <=> aElementOf0(sdtlpdtrp0(xf, xp), xU)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.50 tff(131,plain,
% 0.19/0.50 (aElementOf0(sdtlpdtrp0(xf, xp), xU)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[116, 130])).
% 0.19/0.50 tff(132,plain,
% 0.19/0.50 (szDzozmdt0(xf) = xU),
% 0.19/0.50 inference(transitivity,[status(thm)],[39, 45])).
% 0.19/0.50 tff(133,plain,
% 0.19/0.50 (aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf)) <=> aElementOf0(sdtlpdtrp0(xf, xp), xU)),
% 0.19/0.50 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.50 tff(134,plain,
% 0.19/0.50 (aElementOf0(sdtlpdtrp0(xf, xp), xU) <=> aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))),
% 0.19/0.50 inference(symmetry,[status(thm)],[133])).
% 0.19/0.50 tff(135,plain,
% 0.19/0.50 (aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[131, 134])).
% 0.19/0.50 tff(136,plain,
% 0.19/0.50 (^[W0: $i] : rewrite(((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(137,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.50 tff(138,plain,
% 0.19/0.50 (^[W0: $i] : refl(((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(139,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.50 tff(140,plain,
% 0.19/0.50 (^[W0: $i] : rewrite(((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(141,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.50 tff(142,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.50 tff(143,plain,
% 0.19/0.50 (^[W0: $i] : rewrite(((~aFunction0(W0)) | (((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))) & (isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~(aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0)) & aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))) <=> ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(144,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))) & (isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~(aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0)) & aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.50 tff(145,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(146,plain,
% 0.19/0.50 (^[W0: $i] : trans(monotonicity(rewrite((isMonotone0(W0) <=> ![W1: $i, W2: $i] : ((aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))) => (sdtlseqdt0(W1, W2) => sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2))))) <=> (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))))))), ((aFunction0(W0) => (isMonotone0(W0) <=> ![W1: $i, W2: $i] : ((aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))) => (sdtlseqdt0(W1, W2) => sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)))))) <=> (aFunction0(W0) => (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))))))))), rewrite((aFunction0(W0) => (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))))))) <=> ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))))), ((aFunction0(W0) => (isMonotone0(W0) <=> ![W1: $i, W2: $i] : ((aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))) => (sdtlseqdt0(W1, W2) => sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)))))) <=> ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(147,plain,
% 0.19/0.50 (![W0: $i] : (aFunction0(W0) => (isMonotone0(W0) <=> ![W1: $i, W2: $i] : ((aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))) => (sdtlseqdt0(W1, W2) => sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)))))) <=> ![W0: $i] : ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.50 tff(148,axiom,(![W0: $i] : (aFunction0(W0) => (isMonotone0(W0) <=> ![W1: $i, W2: $i] : ((aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0))) => (sdtlseqdt0(W1, W2) => sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefMonot')).
% 0.19/0.50 tff(149,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.50 tff(150,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (isMonotone0(W0) <=> ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.19/0.50 tff(151,plain,(
% 0.19/0.50 ![W0: $i] : ((~aFunction0(W0)) | (((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~(aElementOf0(W1, szDzozmdt0(W0)) & aElementOf0(W2, szDzozmdt0(W0)))))) & (isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~(aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0)) & aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0)))))))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[150])).
% 0.19/0.50 tff(152,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))) | (~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 (![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[153, 137])).
% 0.19/0.51 tff(155,plain,
% 0.19/0.51 (((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | ((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | (~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(156,plain,
% 0.19/0.51 (((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~(sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))))))) <=> ((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(157,plain,
% 0.19/0.51 (((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | ((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~(sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | ((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.51 tff(158,plain,
% 0.19/0.51 (((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | ((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~(sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | (~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[157, 155])).
% 0.19/0.51 tff(159,plain,
% 0.19/0.51 ((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | ((~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~(sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(160,plain,
% 0.19/0.51 ((~![W0: $i] : ((~aFunction0(W0)) | (~((~(isMonotone0(W0) | (~(sdtlseqdt0(sdtlpdtrp0(W0, tptp_fun_W1_10(W0)), sdtlpdtrp0(W0, tptp_fun_W2_9(W0))) | (~sdtlseqdt0(tptp_fun_W1_10(W0), tptp_fun_W2_9(W0))) | (~aElementOf0(tptp_fun_W1_10(W0), szDzozmdt0(W0))) | (~aElementOf0(tptp_fun_W2_9(W0), szDzozmdt0(W0))))))) | (~((~isMonotone0(W0)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(W0, W1), sdtlpdtrp0(W0, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(W0))) | (~aElementOf0(W2, szDzozmdt0(W0)))))))))) | (~aFunction0(xf)) | (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.51 tff(161,plain,
% 0.19/0.51 (~((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[160, 154, 95])).
% 0.19/0.51 tff(162,plain,
% 0.19/0.51 (((~(isMonotone0(xf) | (~((~aElementOf0(tptp_fun_W2_9(xf), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_10(xf), szDzozmdt0(xf))) | (~sdtlseqdt0(tptp_fun_W1_10(xf), tptp_fun_W2_9(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_10(xf)), sdtlpdtrp0(xf, tptp_fun_W2_9(xf))))))) | (~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))))) | ((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(163,plain,
% 0.19/0.51 ((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.19/0.51 tff(164,plain,
% 0.19/0.51 (isMonotone0(xf) <=> isMonotone0(xf)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(165,plain,
% 0.19/0.51 (isMonotone0(xf)),
% 0.19/0.51 inference(and_elim,[status(thm)],[62])).
% 0.19/0.51 tff(166,plain,
% 0.19/0.51 (isMonotone0(xf)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.51 tff(167,plain,
% 0.19/0.51 ((~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))) | (~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(168,plain,
% 0.19/0.51 ((~((~isMonotone0(xf)) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf)))))) | ![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.51 tff(169,plain,
% 0.19/0.51 (![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[168, 163])).
% 0.19/0.51 tff(170,plain,
% 0.19/0.51 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) <=> aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(171,axiom,(((![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)) & aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)) & ![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))) & aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1299')).
% 0.19/0.51 tff(172,plain,
% 0.19/0.51 ((![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)) & aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)) & ![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))),
% 0.19/0.51 inference(and_elim,[status(thm)],[171])).
% 0.19/0.51 tff(173,plain,
% 0.19/0.51 (![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)) & aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.19/0.51 inference(and_elim,[status(thm)],[172])).
% 0.19/0.51 tff(174,plain,
% 0.19/0.51 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.19/0.51 inference(and_elim,[status(thm)],[173])).
% 0.19/0.51 tff(175,plain,
% 0.19/0.51 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.19/0.51 tff(176,plain,
% 0.19/0.51 (((~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)) | (~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU))),
% 0.19/0.51 inference(tautology,[status(thm)],[])).
% 0.19/0.51 tff(177,plain,
% 0.19/0.51 ((~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.51 tff(178,plain,
% 0.19/0.51 (^[W0: $i] : refl((sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU)))) <=> (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(179,plain,
% 0.19/0.51 (![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU)))) <=> ![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.51 tff(180,plain,
% 0.19/0.51 (^[W0: $i] : trans(monotonicity(rewrite((((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU))) <=> (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU)))), ((sdtlseqdt0(W0, xp) | (((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU)))) <=> (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU)))))), rewrite((sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU)))) <=> (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))), ((sdtlseqdt0(W0, xp) | (((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU)))) <=> (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(181,plain,
% 0.19/0.51 (![W0: $i] : (sdtlseqdt0(W0, xp) | (((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU)))) <=> ![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[180])).
% 0.19/0.51 tff(182,plain,
% 0.19/0.51 (^[W0: $i] : rewrite(((((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp)) <=> (sdtlseqdt0(W0, xp) | (((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU)))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(183,plain,
% 0.19/0.51 (![W0: $i] : ((((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp)) <=> ![W0: $i] : (sdtlseqdt0(W0, xp) | (((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[182])).
% 0.19/0.51 tff(184,plain,
% 0.19/0.51 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp)) <=> ![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(185,plain,
% 0.19/0.51 (^[W0: $i] : trans(monotonicity(rewrite(((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) <=> ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))), ((((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> (((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)))), rewrite((((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))), ((((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(186,plain,
% 0.19/0.51 (![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> ![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[185])).
% 0.19/0.51 tff(187,plain,
% 0.19/0.51 (![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))),
% 0.19/0.51 inference(and_elim,[status(thm)],[51])).
% 0.19/0.51 tff(188,plain,
% 0.19/0.51 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.51 tff(189,plain,
% 0.19/0.51 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.19/0.51 tff(190,plain,(
% 0.19/0.51 ![W0: $i] : ((((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.19/0.51 inference(skolemize,[status(sab)],[189])).
% 0.19/0.51 tff(191,plain,
% 0.19/0.51 (![W0: $i] : (sdtlseqdt0(W0, xp) | (((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, xP, xU))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[190, 183])).
% 0.19/0.51 tff(192,plain,
% 0.19/0.51 (![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[191, 181])).
% 0.19/0.51 tff(193,plain,
% 0.19/0.51 (![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[192, 179])).
% 0.19/0.51 tff(194,plain,
% 0.19/0.51 (((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))) | (sdtlseqdt0(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU))))) <=> ((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(195,plain,
% 0.19/0.51 ((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))) | (sdtlseqdt0(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(196,plain,
% 0.19/0.51 ((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~aElementOf0(W0, xU)) | (~((~aElementOf0(tptp_fun_W1_16(W0), xP)) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, xP, xU))))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.51 tff(197,plain,
% 0.19/0.51 (sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[196, 193, 177])).
% 0.19/0.51 tff(198,plain,
% 0.19/0.51 (((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))))) <=> ((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(199,plain,
% 0.19/0.52 ((sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~aElementOf0(xp, szDzozmdt0(xf)))) <=> ((~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(200,plain,
% 0.19/0.52 (((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | (sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~aElementOf0(xp, szDzozmdt0(xf))))) <=> ((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf)))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[199])).
% 0.19/0.52 tff(201,plain,
% 0.19/0.52 (((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | (sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~aElementOf0(xp, szDzozmdt0(xf))))) <=> ((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[200, 198])).
% 0.19/0.52 tff(202,plain,
% 0.19/0.52 ((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | (sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~aElementOf0(xp, szDzozmdt0(xf))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(203,plain,
% 0.19/0.52 ((~![W1: $i, W2: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W1), sdtlpdtrp0(xf, W2)) | (~sdtlseqdt0(W1, W2)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W2, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.52 tff(204,plain,
% 0.19/0.52 (sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[203, 57, 197, 169, 135])).
% 0.19/0.52 tff(205,plain,
% 0.19/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) <=> aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(206,plain,
% 0.19/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)),
% 0.19/0.52 inference(and_elim,[status(thm)],[171])).
% 0.19/0.52 tff(207,plain,
% 0.19/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.19/0.52 tff(208,plain,
% 0.19/0.52 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(209,plain,
% 0.19/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.19/0.52 tff(210,plain,
% 0.19/0.52 ((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(211,plain,
% 0.19/0.52 ((~((~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)))))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xU)) | aElementOf0(sdtlpdtrp0(xf, xp), xP)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.19/0.52 tff(212,plain,
% 0.19/0.52 (aElementOf0(sdtlpdtrp0(xf, xp), xP)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[211, 204, 131, 129])).
% 0.19/0.52 tff(213,plain,
% 0.19/0.52 (^[W0: $i] : refl(((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)) <=> ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(214,plain,
% 0.19/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[213])).
% 0.19/0.52 tff(215,plain,
% 0.19/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(216,plain,
% 0.19/0.52 (^[W0: $i] : rewrite((aElementOf0(W0, xP) => sdtlseqdt0(xp, W0)) <=> ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(217,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[216])).
% 0.19/0.52 tff(218,plain,
% 0.19/0.52 (![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(and_elim,[status(thm)],[53])).
% 0.19/0.52 tff(219,plain,
% 0.19/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.19/0.52 tff(220,plain,
% 0.19/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.19/0.52 tff(221,plain,(
% 0.19/0.52 ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(skolemize,[status(sab)],[220])).
% 0.19/0.52 tff(222,plain,
% 0.19/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.19/0.52 tff(223,plain,
% 0.19/0.52 (((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(224,plain,
% 0.19/0.52 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(225,plain,
% 0.19/0.52 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | (~aElementOf0(sdtlpdtrp0(xf, xp), xP)) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.19/0.52 tff(226,plain,
% 0.19/0.52 (sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[225, 222, 212])).
% 0.19/0.52 tff(227,plain,
% 0.19/0.52 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0))) <=> ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(228,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[227])).
% 0.19/0.52 tff(229,plain,
% 0.19/0.52 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) <=> (~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> (~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))))), rewrite((~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), 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))))), (((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ((W0 = W1) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite(((W0 = W1) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))), (((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(230,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[229])).
% 0.19/0.52 tff(231,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(232,plain,
% 0.19/0.52 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))), (((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((aElement0(W0) & aElement0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))))), rewrite(((aElement0(W0) & aElement0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))), (((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))))),
% 0.19/0.52 inference(bind,[status(th)],[])).
% 0.19/0.52 tff(233,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.19/0.52 inference(quant_intro,[status(thm)],[232])).
% 0.19/0.52 tff(234,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mASymm')).
% 0.19/0.52 tff(235,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.52 tff(236,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.19/0.52 tff(237,plain,(
% 0.19/0.52 ![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.19/0.52 inference(skolemize,[status(sab)],[236])).
% 0.19/0.52 tff(238,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.19/0.52 tff(239,plain,
% 0.19/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.19/0.52 tff(240,plain,
% 0.19/0.52 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(241,plain,
% 0.19/0.52 (((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp))) <=> ((~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(242,plain,
% 0.19/0.52 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[241])).
% 0.19/0.52 tff(243,plain,
% 0.19/0.52 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.19/0.52 inference(transitivity,[status(thm)],[242, 240])).
% 0.19/0.52 tff(244,plain,
% 0.19/0.52 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(245,plain,
% 0.19/0.52 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.19/0.52 tff(246,plain,
% 0.19/0.52 ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[245, 239, 197])).
% 0.19/0.52 tff(247,plain,
% 0.19/0.52 (xp = sdtlpdtrp0(xf, xp)),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[246, 226, 120, 92])).
% 0.19/0.52 tff(248,plain,
% 0.19/0.52 (aElementOf0(xp, xP) <=> aElementOf0(sdtlpdtrp0(xf, xp), xP)),
% 0.19/0.52 inference(monotonicity,[status(thm)],[247])).
% 0.19/0.52 tff(249,plain,
% 0.19/0.52 (aElementOf0(sdtlpdtrp0(xf, xp), xP) <=> aElementOf0(xp, xP)),
% 0.19/0.52 inference(symmetry,[status(thm)],[248])).
% 0.19/0.52 tff(250,plain,
% 0.19/0.52 (aElementOf0(xp, xP)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[212, 249])).
% 0.19/0.52 tff(251,plain,
% 0.19/0.52 ((~((~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))))) | (~aElementOf0(xp, xP)) | (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(252,plain,
% 0.19/0.52 (~((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[251, 250, 33])).
% 0.19/0.52 tff(253,plain,
% 0.19/0.52 (((~aElementOf0(xp, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))) | (~aUpperBoundOfIn0(xp, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp))) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))),
% 0.19/0.52 inference(tautology,[status(thm)],[])).
% 0.19/0.52 tff(254,plain,
% 0.19/0.52 (![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, xp))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.19/0.52 tff(255,plain,
% 0.19/0.52 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(256,plain,
% 0.19/0.52 ((~((~(aElementOf0(W0!18, xP) | (~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, xP)) | (~((~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))))))))) <=> (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(257,plain,
% 0.19/0.52 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, xP)) | (~((~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[256])).
% 0.19/0.52 tff(258,plain,
% 0.19/0.52 (((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, xP)) | (~((~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[257, 255])).
% 0.19/0.52 tff(259,plain,
% 0.19/0.52 ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, xP)) | (~((~aElementOf0(W0!18, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(260,plain,
% 0.19/0.53 ((~![W0: $i] : (~((~(aElementOf0(W0, xP) | (~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, xU) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, xP)) | (~((~aElementOf0(W0, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, xU)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.19/0.53 tff(261,plain,
% 0.19/0.53 (~((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[260, 24])).
% 0.19/0.53 tff(262,plain,
% 0.19/0.53 (((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~((~aElementOf0(W0!18, xP)) | (~((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xU)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU))))))) | (aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(263,plain,
% 0.19/0.53 (aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.19/0.53 tff(264,plain,
% 0.19/0.53 (aElementOf0(W0!18, xU) <=> aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.53 tff(265,plain,
% 0.19/0.53 (aElementOf0(W0!18, szDzozmdt0(xf)) <=> aElementOf0(W0!18, xU)),
% 0.19/0.53 inference(symmetry,[status(thm)],[264])).
% 0.19/0.53 tff(266,plain,
% 0.19/0.53 (^[W0: $i] : refl((~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS))))) <=> (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(267,plain,
% 0.19/0.53 (![W0: $i] : (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[266])).
% 0.19/0.53 tff(268,plain,
% 0.19/0.53 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) <=> ((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))), rewrite(((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)) <=> ((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS))), ((((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> (((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf))))) & ((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS))))), rewrite((((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf))))) & ((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS))) <=> (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))), ((((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(269,plain,
% 0.19/0.53 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[268])).
% 0.19/0.53 tff(270,plain,
% 0.19/0.53 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> ![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(271,plain,
% 0.19/0.53 (^[W0: $i] : rewrite(((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS))) <=> (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(272,plain,
% 0.19/0.53 (![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS))) <=> ![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[271])).
% 0.19/0.53 tff(273,axiom,((aSet0(xS) & ![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS)))) & (xS = cS1142(xf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1144')).
% 0.19/0.53 tff(274,plain,
% 0.19/0.53 (aSet0(xS) & ![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS)))),
% 0.19/0.53 inference(and_elim,[status(thm)],[273])).
% 0.19/0.53 tff(275,plain,
% 0.19/0.53 (![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS)))),
% 0.19/0.53 inference(and_elim,[status(thm)],[274])).
% 0.19/0.53 tff(276,plain,
% 0.19/0.53 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[275, 272])).
% 0.19/0.53 tff(277,plain,
% 0.19/0.53 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[276, 270])).
% 0.19/0.53 tff(278,plain,(
% 0.19/0.53 ![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.19/0.53 inference(skolemize,[status(sab)],[277])).
% 0.19/0.53 tff(279,plain,
% 0.19/0.53 (![W0: $i] : (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[278, 269])).
% 0.19/0.53 tff(280,plain,
% 0.19/0.53 (![W0: $i] : (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[279, 267])).
% 0.19/0.53 tff(281,plain,
% 0.19/0.53 ((~![W0: $i] : (~((~((~aElementOf0(W0, xS)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, xS)))))) | (~((~((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~(aFixedPointOf0(W0!18, xf) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)))))) | aElementOf0(W0!18, xS)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(282,plain,
% 0.19/0.53 (~((~((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~(aFixedPointOf0(W0!18, xf) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)))))) | aElementOf0(W0!18, xS))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.19/0.53 tff(283,plain,
% 0.19/0.53 (((~((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~(aFixedPointOf0(W0!18, xf) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)))))) | aElementOf0(W0!18, xS)))) | ((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(284,plain,
% 0.19/0.53 ((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.19/0.53 tff(285,assumption,(~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~aUpperBoundOfIn0(W0!18, xT, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))))), introduced(assumption)).
% 0.19/0.53 tff(286,plain,
% 0.19/0.53 ((sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~aUpperBoundOfIn0(W0!18, xT, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))) | aElementOf0(W0!18, xS)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(287,plain,
% 0.19/0.53 (aElementOf0(W0!18, xS)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.19/0.53 tff(288,plain,
% 0.19/0.53 ((~((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(289,plain,
% 0.19/0.53 ((~((~aElementOf0(W0!18, xS)) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.19/0.53 tff(290,plain,
% 0.19/0.53 (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[289, 284])).
% 0.19/0.53 tff(291,plain,
% 0.19/0.53 (((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))) | aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(292,plain,
% 0.19/0.53 (aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.19/0.53 tff(293,plain,
% 0.19/0.53 (aElementOf0(W0!18, xU)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[292, 265])).
% 0.19/0.53 tff(294,plain,
% 0.19/0.53 (((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))) | (sdtlpdtrp0(xf, W0!18) = W0!18)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(295,plain,
% 0.19/0.53 (sdtlpdtrp0(xf, W0!18) = W0!18),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[294, 290])).
% 0.19/0.53 tff(296,plain,
% 0.19/0.53 (W0!18 = sdtlpdtrp0(xf, W0!18)),
% 0.19/0.53 inference(symmetry,[status(thm)],[295])).
% 0.19/0.53 tff(297,plain,
% 0.19/0.53 (sdtlseqdt0(W0!18, W0!18) <=> sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[296])).
% 0.19/0.53 tff(298,plain,
% 0.19/0.53 ((xS = cS1142(xf)) <=> (xS = cS1142(xf))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(299,plain,
% 0.19/0.53 (xS = cS1142(xf)),
% 0.19/0.53 inference(and_elim,[status(thm)],[273])).
% 0.19/0.53 tff(300,plain,
% 0.19/0.53 (xS = cS1142(xf)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.19/0.53 tff(301,plain,
% 0.19/0.53 (cS1142(xf) = xS),
% 0.19/0.53 inference(symmetry,[status(thm)],[300])).
% 0.19/0.53 tff(302,plain,
% 0.19/0.53 (aElementOf0(W0!18, cS1142(xf)) <=> aElementOf0(W0!18, xS)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[301])).
% 0.19/0.53 tff(303,plain,
% 0.19/0.53 (aElementOf0(W0!18, xS) <=> aElementOf0(W0!18, cS1142(xf))),
% 0.19/0.53 inference(symmetry,[status(thm)],[302])).
% 0.19/0.53 tff(304,plain,
% 0.19/0.53 (aElementOf0(W0!18, cS1142(xf))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[287, 303])).
% 0.19/0.53 tff(305,plain,
% 0.19/0.53 (aSet0(cS1142(xf)) <=> aSet0(xS)),
% 0.19/0.53 inference(monotonicity,[status(thm)],[301])).
% 0.19/0.53 tff(306,plain,
% 0.19/0.53 (aSet0(xS) <=> aSet0(cS1142(xf))),
% 0.19/0.53 inference(symmetry,[status(thm)],[305])).
% 0.19/0.53 tff(307,plain,
% 0.19/0.53 (aSet0(xS) <=> aSet0(xS)),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(308,plain,
% 0.19/0.53 (aSet0(xS)),
% 0.19/0.53 inference(and_elim,[status(thm)],[274])).
% 0.19/0.53 tff(309,plain,
% 0.19/0.53 (aSet0(xS)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.53 tff(310,plain,
% 0.19/0.53 (aSet0(cS1142(xf))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[309, 306])).
% 0.19/0.53 tff(311,plain,
% 0.19/0.53 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf)))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf)))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(312,plain,
% 0.19/0.53 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf)))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(313,plain,
% 0.19/0.53 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.19/0.53 tff(314,plain,
% 0.19/0.53 ((~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[313, 82])).
% 0.19/0.53 tff(315,plain,
% 0.19/0.53 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[314, 310])).
% 0.19/0.53 tff(316,plain,
% 0.19/0.53 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | (aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(317,plain,
% 0.19/0.53 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | (aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(318,plain,
% 0.19/0.53 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf)))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.19/0.53 tff(319,plain,
% 0.19/0.53 (aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[318, 315])).
% 0.19/0.53 tff(320,plain,
% 0.19/0.53 (aElement0(W0!18)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[319, 304])).
% 0.19/0.53 tff(321,plain,
% 0.19/0.53 (^[W0: $i] : refl(((~aElement0(W0)) | sdtlseqdt0(W0, W0)) <=> ((~aElement0(W0)) | sdtlseqdt0(W0, W0)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(322,plain,
% 0.19/0.53 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0)) <=> ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[321])).
% 0.19/0.53 tff(323,plain,
% 0.19/0.53 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0)) <=> ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(324,plain,
% 0.19/0.53 (^[W0: $i] : rewrite((aElement0(W0) => sdtlseqdt0(W0, W0)) <=> ((~aElement0(W0)) | sdtlseqdt0(W0, W0)))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(325,plain,
% 0.19/0.53 (![W0: $i] : (aElement0(W0) => sdtlseqdt0(W0, W0)) <=> ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[324])).
% 0.19/0.53 tff(326,axiom,(![W0: $i] : (aElement0(W0) => sdtlseqdt0(W0, W0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mARefl')).
% 0.19/0.53 tff(327,plain,
% 0.19/0.53 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.19/0.53 tff(328,plain,
% 0.19/0.53 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.19/0.53 tff(329,plain,(
% 0.19/0.53 ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(skolemize,[status(sab)],[328])).
% 0.19/0.53 tff(330,plain,
% 0.19/0.53 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[329, 322])).
% 0.19/0.53 tff(331,plain,
% 0.19/0.53 (((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | ((~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18))) <=> ((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | (~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(332,plain,
% 0.19/0.53 ((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | ((~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(333,plain,
% 0.19/0.53 ((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | (~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.19/0.53 tff(334,plain,
% 0.19/0.53 (sdtlseqdt0(W0!18, W0!18)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[333, 330, 320])).
% 0.19/0.53 tff(335,plain,
% 0.19/0.53 (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[334, 297])).
% 0.19/0.53 tff(336,plain,
% 0.19/0.53 ((sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~aUpperBoundOfIn0(W0!18, xT, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))) | (~sdtlseqdt0(xp, W0!18))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(337,plain,
% 0.19/0.53 (~sdtlseqdt0(xp, W0!18)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[336, 285])).
% 0.19/0.53 tff(338,plain,
% 0.19/0.53 (((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(W0!18, xP)) | sdtlseqdt0(xp, W0!18))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | (~aElementOf0(W0!18, xP)) | sdtlseqdt0(xp, W0!18))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(339,plain,
% 0.19/0.53 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(W0!18, xP)) | sdtlseqdt0(xp, W0!18))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(340,plain,
% 0.19/0.53 ((~![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))) | (~aElementOf0(W0!18, xP)) | sdtlseqdt0(xp, W0!18)),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.19/0.53 tff(341,plain,
% 0.19/0.53 (~aElementOf0(W0!18, xP)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[340, 222, 337])).
% 0.19/0.53 tff(342,plain,
% 0.19/0.53 ((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(343,plain,
% 0.19/0.53 ((~(aElementOf0(W0!18, xP) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aElementOf0(W0!18, xU)) | (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[342, 341])).
% 0.19/0.53 tff(344,plain,
% 0.19/0.53 (~(aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[343, 335, 293, 263])).
% 0.19/0.53 tff(345,plain,
% 0.19/0.53 ((aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT))) | aElementOf0(tptp_fun_W1_15(W0!18), xT)),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(346,plain,
% 0.19/0.53 (aElementOf0(tptp_fun_W1_15(W0!18), xT)),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[345, 344])).
% 0.19/0.53 tff(347,plain,
% 0.19/0.53 ((aUpperBoundOfIn0(W0!18, xT, xU) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT))) | (~sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(348,plain,
% 0.19/0.54 (~sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[347, 344])).
% 0.19/0.54 tff(349,plain,
% 0.19/0.54 ((sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~aUpperBoundOfIn0(W0!18, xT, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(350,plain,
% 0.19/0.54 (![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[349, 285])).
% 0.19/0.54 tff(351,plain,
% 0.19/0.54 (((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | ((~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(352,plain,
% 0.19/0.54 ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | ((~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(353,plain,
% 0.19/0.54 ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.19/0.54 tff(354,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[353, 350, 348, 346])).
% 0.19/0.54 tff(355,plain,(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~aUpperBoundOfIn0(W0!18, xT, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.54 tff(356,plain,
% 0.19/0.54 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(357,plain,
% 0.19/0.54 (((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp)))) <=> ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(358,plain,
% 0.19/0.54 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[357])).
% 0.19/0.54 tff(359,plain,
% 0.19/0.54 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.19/0.54 inference(transitivity,[status(thm)],[358, 356])).
% 0.19/0.54 tff(360,plain,
% 0.19/0.54 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(361,plain,
% 0.19/0.54 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.19/0.54 tff(362,plain,
% 0.19/0.54 ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[361, 239, 197])).
% 0.19/0.54 tff(363,plain,
% 0.19/0.54 (sdtlpdtrp0(xf, xp) = xp),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[362, 226, 120, 92])).
% 0.19/0.54 tff(364,plain,
% 0.19/0.54 ((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(365,plain,
% 0.19/0.54 (~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[364, 363, 57])).
% 0.19/0.54 tff(366,plain,
% 0.19/0.54 (((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf)) | ((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(367,plain,
% 0.19/0.54 ((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[366, 365])).
% 0.19/0.54 tff(368,plain,
% 0.19/0.54 (((~((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, xS) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xS)))))) | aSupremumOfIn0(xp, xT, xS)))) <=> ((~((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, xS) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~aUpperBoundOfIn0(W0!18, xT, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))))))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(369,plain,
% 0.19/0.54 (((~((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, xS) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xS)))))) | aSupremumOfIn0(xp, xT, xS)))) <=> ((~((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, xS) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xS)))))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(370,plain,
% 0.19/0.54 (((~((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf))) | ((((~aUpperBoundOfIn0(xp, xT, xS)) & (~((~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp)))) | (aElementOf0(W0!18, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)) & aUpperBoundOfIn0(W0!18, xT, xS) & (~sdtlseqdt0(xp, W0!18)))) & (~aSupremumOfIn0(xp, xT, xS)))) <=> ((~((~((~aElementOf0(xp, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, xp) = xp)))) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, xS) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, xS)) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, xS)))))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(371,plain,
% 0.19/0.54 (((~((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf))) | ((((~aUpperBoundOfIn0(xp, xT, xS)) & (~((~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp)))) | ((aElementOf0(W0!18, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)) & aUpperBoundOfIn0(W0!18, xT, xS)) & (~sdtlseqdt0(xp, W0!18)))) & (~aSupremumOfIn0(xp, xT, xS)))) <=> ((~((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf))) | ((((~aUpperBoundOfIn0(xp, xT, xS)) & (~((~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp)))) | (aElementOf0(W0!18, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)) & aUpperBoundOfIn0(W0!18, xT, xS) & (~sdtlseqdt0(xp, W0!18)))) & (~aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(372,plain,
% 0.19/0.54 ((((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))) <=> (((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(373,plain,
% 0.19/0.54 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[372])).
% 0.19/0.54 tff(374,plain,
% 0.19/0.54 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(375,plain,
% 0.19/0.54 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, xp)) | aUpperBoundOfIn0(xp, xT, xS)) & ![W0: $i] : (((aElementOf0(W0, xS) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xS)) => sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(376,axiom,(~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, xp)) | aUpperBoundOfIn0(xp, xT, xS)) & ![W0: $i] : (((aElementOf0(W0, xS) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xS)) => sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.55 tff(377,plain,
% 0.19/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.19/0.55 tff(378,plain,
% 0.19/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[377, 373])).
% 0.19/0.55 tff(379,plain,
% 0.19/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[378, 374])).
% 0.19/0.55 tff(380,plain,
% 0.19/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[379, 373])).
% 0.19/0.55 unexpected number of arguments: (let ((a!1 (or (and (aElementOf0 xp (szDzozmdt0 xf)) (= (sdtlpdtrp0 xf xp) xp))
% 0.19/0.55 (aFixedPointOf0 xp xf)))
% 0.19/0.55 (a!2 (refl (~ (not (aUpperBoundOfIn0 xp xT xS))
% 0.19/0.55 (not (aUpperBoundOfIn0 xp xT xS)))))
% 0.19/0.55 (a!3 (forall ((W0 $i)) (or (not (aElementOf0 W0 xT)) (sdtlseqdt0 W0 xp))))
% 0.19/0.55 (a!4 (not (or (not (aElementOf0 W0!17 xT)) (sdtlseqdt0 W0!17 xp))))
% 0.19/0.55 (a!7 (forall ((W0 $i))
% 0.19/0.55 (let ((a!1 (forall ((W1 $i))
% 0.19/0.55 (or (not (aElementOf0 W1 xT)) (sdtlseqdt0 W1 W0)))))
% 0.19/0.55 (or (not (and (aElementOf0 W0 xS)
% 0.19/0.55 a!1
% 0.19/0.55 (aUpperBoundOfIn0 W0 xT xS)))
% 0.19/0.55 (sdtlseqdt0 xp W0)))))
% 0.19/0.55 (a!8 (forall ((W1 $i))
% 0.19/0.55 (or (not (aElementOf0 W1 xT)) (sdtlseqdt0 W1 W0!18))))
% 0.19/0.55 (a!14 (refl (~ (not (sdtlseqdt0 xp W0!18)) (not (sdtlseqdt0 xp W0!18)))))
% 0.19/0.55 (a!20 (refl (~ (not (aSupremumOfIn0 xp xT xS))
% 0.19/0.55 (not (aSupremumOfIn0 xp xT xS))))))
% 0.19/0.55 (let ((a!5 (~ (not (or (aUpperBoundOfIn0 xp xT xS) a!3))
% 0.19/0.55 (and (not (aUpperBoundOfIn0 xp xT xS)) a!4)))
% 0.19/0.55 (a!9 (not (and (aElementOf0 W0!18 xS) a!8 (aUpperBoundOfIn0 W0!18 xT xS))))
% 0.19/0.55 (a!11 (nnf-pos (proof-bind (lambda ((W1 $i))
% 0.19/0.55 (let ((a!1 (~ (or (not (aElementOf0 W1 xT))
% 0.19/0.55 (sdtlseqdt0 W1 W0!18))
% 0.19/0.55 (or (not (aElementOf0 W1 xT))
% 0.19/0.55 (sdtlseqdt0 W1 W0!18)))))
% 0.19/0.55 (refl a!1))))
% 0.19/0.55 (~ a!8 a!8)))
% 0.19/0.55 (a!15 (and (and (aElementOf0 W0!18 xS) a!8 (aUpperBoundOfIn0 W0!18 xT xS))
% 0.19/0.55 (not (sdtlseqdt0 xp W0!18))))
% 0.19/0.55 (a!17 (not (and (or (aUpperBoundOfIn0 xp xT xS) a!3) a!7)))
% 0.19/0.55 (a!21 (or (and (or (aUpperBoundOfIn0 xp xT xS) a!3) a!7)
% 0.19/0.55 (aSupremumOfIn0 xp xT xS))))
% 0.19/0.55 (let ((a!6 (nnf-neg a!2 (sk (~ (not a!3) a!4)) a!5))
% 0.19/0.55 (a!10 (~ (not a!7) (not (or a!9 (sdtlseqdt0 xp W0!18)))))
% 0.19/0.55 (a!12 (monotonicity (refl (~ (aElementOf0 W0!18 xS)
% 0.19/0.55 (aElementOf0 W0!18 xS)))
% 0.19/0.55 a!11
% 0.19/0.55 (refl (~ (aUpperBoundOfIn0 W0!18 xT xS)
% 0.19/0.55 (aUpperBoundOfIn0 W0!18 xT xS)))
% 0.19/0.55 (~ (and (aElementOf0 W0!18 xS)
% 0.19/0.55 a!8
% 0.19/0.55 (aUpperBoundOfIn0 W0!18 xT xS))
% 0.19/0.55 (and (aElementOf0 W0!18 xS)
% 0.19/0.55 a!8
% 0.19/0.55 (aUpperBoundOfIn0 W0!18 xT xS)))))
% 0.19/0.55 (a!16 (~ (not (or a!9 (sdtlseqdt0 xp W0!18))) a!15))
% 0.19/0.55 (a!18 (or (and (not (aUpperBoundOfIn0 xp xT xS)) a!4) a!15)))
% 0.19/0.55 (let ((a!13 (nnf-neg a!12
% 0.19/0.55 (~ (not a!9)
% 0.19/0.55 (and (aElementOf0 W0!18 xS)
% 0.19/0.55 a!8
% 0.19/0.55 (aUpperBoundOfIn0 W0!18 xT xS)))))
% 0.19/0.55 (a!22 (~ (not a!21) (and a!18 (not (aSupremumOfIn0 xp xT xS)))))
% 0.19/0.55 (a!23 (or (not a!1) (and a!18 (not (aSupremumOfIn0 xp xT xS))))))
% 0.19/0.55 (let ((a!19 (nnf-neg a!6
% 0.19/0.55 (trans (sk a!10)
% 0.19/0.55 (nnf-neg a!13 a!14 a!16)
% 0.19/0.55 (~ (not a!7) a!15))
% 0.19/0.55 (~ a!17 a!18))))
% 0.19/0.55 (nnf-neg (refl (~ (not a!1) (not a!1)))
% 0.19/0.55 (nnf-neg a!19 a!20 a!22)
% 0.19/0.55 (~ (not (and a!1 a!21)) a!23)))))))
% 0.19/0.55 Proof display could not be completed: unexpected number of arguments
% 0.19/0.55 % E exiting
%------------------------------------------------------------------------------