%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM547+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:21:21 AM UTC 2025
% Result : Theorem 3.15s 3.32s
% Output : Proof 3.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM547+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 01:24:20 EDT 2025
% 0.14/0.34 % CPUTime :
% 3.15/3.32 % SZS status Theorem
% 3.15/3.32 % SZS output start Proof
% 3.15/3.32 tff(aElementOf0_type, type, (
% 3.15/3.32 aElementOf0: ( $i * $i ) > $o)).
% 3.15/3.32 tff(slbdtsldtrb0_type, type, (
% 3.15/3.32 slbdtsldtrb0: ( $i * $i ) > $i)).
% 3.15/3.32 tff(xk_type, type, (
% 3.15/3.32 xk: $i)).
% 3.15/3.32 tff(xS_type, type, (
% 3.15/3.32 xS: $i)).
% 3.15/3.32 tff(sbrdtbr0_type, type, (
% 3.15/3.32 sbrdtbr0: $i > $i)).
% 3.15/3.32 tff(aSubsetOf0_type, type, (
% 3.15/3.32 aSubsetOf0: ( $i * $i ) > $o)).
% 3.15/3.32 tff(aSet0_type, type, (
% 3.15/3.32 aSet0: $i > $o)).
% 3.15/3.32 tff(tptp_fun_W1_0_type, type, (
% 3.15/3.32 tptp_fun_W1_0: $i > $i)).
% 3.15/3.32 tff(slcrc0_type, type, (
% 3.15/3.32 slcrc0: $i)).
% 3.15/3.32 tff(xT_type, type, (
% 3.15/3.32 xT: $i)).
% 3.15/3.32 tff(tptp_fun_W3_10_type, type, (
% 3.15/3.32 tptp_fun_W3_10: ( $i * $i * $i ) > $i)).
% 3.15/3.32 tff(sz00_type, type, (
% 3.15/3.32 sz00: $i)).
% 3.15/3.32 tff(szNzAzT0_type, type, (
% 3.15/3.32 szNzAzT0: $i)).
% 3.15/3.32 tff(1,assumption,((~((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))) | (~((~(slbdtsldtrb0(xS, xk) = slcrc0)) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W1: $i] : (~aElementOf0(W1, slbdtsldtrb0(xS, xk))))))))), introduced(assumption)).
% 3.15/3.32 tff(2,plain,
% 3.15/3.32 (^[W0: $i] : rewrite((~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(3,plain,
% 3.15/3.32 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[2])).
% 3.15/3.32 tff(4,plain,
% 3.15/3.32 (^[W0: $i] : refl((~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(5,plain,
% 3.15/3.32 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[4])).
% 3.15/3.32 tff(6,plain,
% 3.15/3.32 (^[W0: $i] : rewrite((~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(7,plain,
% 3.15/3.32 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[6])).
% 3.15/3.32 tff(8,plain,
% 3.15/3.32 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[7, 5])).
% 3.15/3.32 tff(9,plain,
% 3.15/3.32 (^[W0: $i] : trans(monotonicity(rewrite(((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) <=> ((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))), rewrite(((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)) <=> ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))), ((((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> (((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))), rewrite((((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))), ((((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(10,plain,
% 3.15/3.32 (![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) <=> ![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[9])).
% 3.15/3.32 tff(11,plain,
% 3.15/3.32 (^[W0: $i] : rewrite((((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | ((~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))) <=> (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(12,plain,
% 3.15/3.32 (![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | ((~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))) <=> ![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[11])).
% 3.15/3.32 tff(13,plain,
% 3.15/3.32 (![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0)))) <=> ![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(14,axiom,(![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefEmp')).
% 3.15/3.32 tff(15,plain,
% 3.15/3.32 (![W0: $i] : ((W0 = slcrc0) <=> (aSet0(W0) & (~?[W1: $i] : aElementOf0(W1, W0))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[14, 13])).
% 3.15/3.32 tff(16,plain,(
% 3.15/3.32 ![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | ((~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))))),
% 3.15/3.32 inference(skolemize,[status(sab)],[15])).
% 3.15/3.32 tff(17,plain,
% 3.15/3.32 (![W0: $i] : (((~(W0 = slcrc0)) | (aSet0(W0) & ![W1: $i] : (~aElementOf0(W1, W0)))) & ((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[16, 12])).
% 3.15/3.32 tff(18,plain,
% 3.15/3.32 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[17, 10])).
% 3.15/3.32 tff(19,plain,
% 3.15/3.32 (![W0: $i] : (~((~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0))))))) | (~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0)))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[18, 8])).
% 3.15/3.32 tff(20,plain,
% 3.15/3.32 (![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[19, 3])).
% 3.15/3.32 tff(21,plain,
% 3.15/3.32 ((~![W0: $i] : (~((~((W0 = slcrc0) | (~aSet0(W0)) | aElementOf0(tptp_fun_W1_0(W0), W0))) | (~((~(W0 = slcrc0)) | (~((~aSet0(W0)) | (~![W1: $i] : (~aElementOf0(W1, W0)))))))))) | (~((~((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))) | (~((~(slbdtsldtrb0(xS, xk) = slcrc0)) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W1: $i] : (~aElementOf0(W1, slbdtsldtrb0(xS, xk))))))))))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(22,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[21, 20, 1])).
% 3.15/3.32 tff(23,plain,(~((~((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))) | (~((~(slbdtsldtrb0(xS, xk) = slcrc0)) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W1: $i] : (~aElementOf0(W1, slbdtsldtrb0(xS, xk)))))))))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(24,plain,
% 3.15/3.32 (((~((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))) | (~((~(slbdtsldtrb0(xS, xk) = slcrc0)) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W1: $i] : (~aElementOf0(W1, slbdtsldtrb0(xS, xk))))))))) | ((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(tautology,[status(thm)],[])).
% 3.15/3.32 tff(25,plain,
% 3.15/3.32 ((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[24, 23])).
% 3.15/3.32 tff(26,assumption,(aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk))), introduced(assumption)).
% 3.15/3.32 tff(27,plain,
% 3.15/3.32 (^[W0: $i] : refl((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) <=> (~aElementOf0(W0, slbdtsldtrb0(xS, xk))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(28,plain,
% 3.15/3.32 (![W0: $i] : (~aElementOf0(W0, slbdtsldtrb0(xS, xk))) <=> ![W0: $i] : (~aElementOf0(W0, slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[27])).
% 3.15/3.32 tff(29,plain,
% 3.15/3.32 ((~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))) <=> (~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(30,axiom,(~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 3.15/3.32 tff(31,plain,
% 3.15/3.32 (~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[30, 29])).
% 3.15/3.32 tff(32,plain,
% 3.15/3.32 (~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[31, 29])).
% 3.15/3.32 tff(33,plain,
% 3.15/3.32 (~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[32, 29])).
% 3.15/3.32 tff(34,plain,
% 3.15/3.32 (~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[33, 29])).
% 3.15/3.32 tff(35,plain,
% 3.15/3.32 (^[W0: $i] : refl($oeq((~aElementOf0(W0, slbdtsldtrb0(xS, xk))), (~aElementOf0(W0, slbdtsldtrb0(xS, xk)))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(36,plain,(
% 3.15/3.32 ![W0: $i] : (~aElementOf0(W0, slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(nnf-neg,[status(sab)],[34, 35])).
% 3.15/3.32 tff(37,plain,
% 3.15/3.32 (![W0: $i] : (~aElementOf0(W0, slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[36, 28])).
% 3.15/3.32 tff(38,plain,
% 3.15/3.32 ((~![W0: $i] : (~aElementOf0(W0, slbdtsldtrb0(xS, xk)))) | (~aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(quant_inst,[status(thm)],[])).
% 3.15/3.32 tff(39,plain,
% 3.15/3.32 ($false),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[38, 37, 26])).
% 3.15/3.32 tff(40,plain,(~aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk))), inference(lemma,lemma(discharge,[]))).
% 3.15/3.32 tff(41,plain,
% 3.15/3.32 ((~(slbdtsldtrb0(xS, xk) = slcrc0)) <=> (~(slbdtsldtrb0(xS, xk) = slcrc0))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(42,axiom,(aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk)) & (~(slbdtsldtrb0(xS, xk) = slcrc0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2227')).
% 3.15/3.32 tff(43,plain,
% 3.15/3.32 (~(slbdtsldtrb0(xS, xk) = slcrc0)),
% 3.15/3.32 inference(and_elim,[status(thm)],[42])).
% 3.15/3.32 tff(44,plain,
% 3.15/3.32 (~(slbdtsldtrb0(xS, xk) = slcrc0)),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[43, 41])).
% 3.15/3.32 tff(45,plain,
% 3.15/3.32 ((~((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))) | (slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(tautology,[status(thm)],[])).
% 3.15/3.32 tff(46,plain,
% 3.15/3.32 ((~((slbdtsldtrb0(xS, xk) = slcrc0) | (~aSet0(slbdtsldtrb0(xS, xk))) | aElementOf0(tptp_fun_W1_0(slbdtsldtrb0(xS, xk)), slbdtsldtrb0(xS, xk)))) | (~aSet0(slbdtsldtrb0(xS, xk)))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[45, 44, 40])).
% 3.15/3.32 tff(47,plain,
% 3.15/3.32 (~aSet0(slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[46, 25])).
% 3.15/3.32 tff(48,plain,
% 3.15/3.32 (((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))) | aSet0(slbdtsldtrb0(xS, xk))),
% 3.15/3.32 inference(tautology,[status(thm)],[])).
% 3.15/3.32 tff(49,plain,
% 3.15/3.32 ((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))),
% 3.15/3.32 inference(unit_resolution,[status(thm)],[48, 47])).
% 3.15/3.32 tff(50,plain,
% 3.15/3.32 (aSet0(xS) <=> aSet0(xS)),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(51,axiom,((aSet0(xS) & aSet0(xT)) & (~(xk = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2202_02')).
% 3.15/3.32 tff(52,plain,
% 3.15/3.32 (aSet0(xS) & aSet0(xT)),
% 3.15/3.32 inference(and_elim,[status(thm)],[51])).
% 3.15/3.32 tff(53,plain,
% 3.15/3.32 (aSet0(xS)),
% 3.15/3.32 inference(and_elim,[status(thm)],[52])).
% 3.15/3.32 tff(54,plain,
% 3.15/3.32 (aSet0(xS)),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[53, 50])).
% 3.15/3.32 tff(55,plain,
% 3.15/3.32 (aElementOf0(xk, szNzAzT0) <=> aElementOf0(xk, szNzAzT0)),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(56,axiom,(aElementOf0(xk, szNzAzT0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2202')).
% 3.15/3.32 tff(57,plain,
% 3.15/3.32 (aElementOf0(xk, szNzAzT0)),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.15/3.32 tff(58,plain,
% 3.15/3.32 (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))) <=> (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))), (![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))) <=> ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))), (((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2))))))))))))), rewrite(((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))), (((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(59,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[58])).
% 3.15/3.32 tff(60,plain,
% 3.15/3.32 (^[W0: $i, W1: $i] : refl(((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(61,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[60])).
% 3.15/3.32 tff(62,plain,
% 3.15/3.32 (^[W0: $i, W1: $i] : rewrite(((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(63,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[62])).
% 3.15/3.32 tff(64,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))),
% 3.15/3.32 inference(transitivity,[status(thm)],[63, 61])).
% 3.15/3.32 tff(65,plain,
% 3.15/3.32 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElementOf0(W1, szNzAzT0)) <=> (~((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0))))), ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) <=> (~(~((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0))))))), rewrite((~(~((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0))))) <=> ((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0)))), ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) <=> ((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) <=> ((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)) <=> (~((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))), ((aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> (aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (~((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))))), rewrite((aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (~((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))) <=> (~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> (~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))), rewrite((~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))) <=> (~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> (~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))), ((~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))) <=> (~(~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))), rewrite((~(~(((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) <=> (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))), ((~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))) <=> (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))), (((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))) <=> ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))), rewrite(((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))) <=> ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))), (((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))) <=> ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))), ((((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))) <=> (((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2))))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))), rewrite((((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2))))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) <=> (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))), ((((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))) <=> (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))))), (![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))) <=> ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))))) <=> (((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))))), rewrite((((~aSet0(W0)) | (~aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(66,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))))) <=> ![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[65])).
% 3.15/3.32 tff(67,plain,
% 3.15/3.32 (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))))) <=> ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(68,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[67])).
% 3.15/3.32 tff(69,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1)))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(70,plain,
% 3.15/3.32 (^[W0: $i, W1: $i] : rewrite(((aSet0(W0) & aElementOf0(W1, szNzAzT0)) => ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1)))))) <=> ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1)))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(71,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((aSet0(W0) & aElementOf0(W1, szNzAzT0)) => ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1)))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))))),
% 3.15/3.32 inference(quant_intro,[status(thm)],[70])).
% 3.15/3.32 tff(72,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElementOf0(W1, szNzAzT0)) => ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSel')).
% 3.15/3.32 tff(73,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[72, 71])).
% 3.15/3.32 tff(74,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : ((W2 = slbdtsldtrb0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[73, 69])).
% 3.15/3.32 tff(75,plain,(
% 3.15/3.32 ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))))))))),
% 3.15/3.32 inference(skolemize,[status(sab)],[74])).
% 3.15/3.32 tff(76,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElementOf0(W1, szNzAzT0))) | ![W2: $i] : (((~(W2 = slbdtsldtrb0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & (sbrdtbr0(W3) = W1))))) & ((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2) <=> (aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0) & (sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1)))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[75, 68])).
% 3.15/3.32 tff(77,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[76, 66])).
% 3.15/3.32 tff(78,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[77, 64])).
% 3.15/3.32 tff(79,plain,
% 3.15/3.32 (![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.32 inference(modus_ponens,[status(thm)],[78, 59])).
% 3.15/3.32 tff(80,plain,
% 3.15/3.32 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(81,plain,
% 3.15/3.32 (((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.32 inference(rewrite,[status(thm)],[])).
% 3.15/3.32 tff(82,plain,
% 3.15/3.32 (^[W2: $i] : rewrite((~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.32 inference(bind,[status(th)],[])).
% 3.15/3.32 tff(83,plain,
% 3.15/3.32 (![W2: $i] : (~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))),
% 3.15/3.33 inference(quant_intro,[status(thm)],[82])).
% 3.15/3.33 tff(84,plain,
% 3.15/3.33 (((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[83])).
% 3.15/3.33 tff(85,plain,
% 3.15/3.33 (((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.33 inference(transitivity,[status(thm)],[84, 81])).
% 3.15/3.33 tff(86,plain,
% 3.15/3.33 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | ((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[85])).
% 3.15/3.33 tff(87,plain,
% 3.15/3.33 (((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | ((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.33 inference(transitivity,[status(thm)],[86, 80])).
% 3.15/3.33 tff(88,plain,
% 3.15/3.33 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | ((~aElementOf0(xk, szNzAzT0)) | (~aSet0(xS)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(xS, xk)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2)))))))))))),
% 3.15/3.33 inference(quant_inst,[status(thm)],[])).
% 3.15/3.33 tff(89,plain,
% 3.15/3.33 ((~![W0: $i, W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~aSet0(W0)) | ![W2: $i] : (~((~((W2 = slbdtsldtrb0(W0, W1)) | (~aSet0(W2)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, W1, W0), W0)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, W1, W0)) = W1))) <=> aElementOf0(tptp_fun_W3_10(W2, W1, W0), W2)))) | (~((~(W2 = slbdtsldtrb0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, W0)) | (~(sbrdtbr0(W3) = W1))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElementOf0(xk, szNzAzT0)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))),
% 3.15/3.33 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.15/3.33 tff(90,plain,
% 3.15/3.33 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))),
% 3.15/3.33 inference(unit_resolution,[status(thm)],[89, 79, 57, 54])).
% 3.15/3.33 tff(91,plain,
% 3.15/3.33 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk))))))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(92,plain,
% 3.15/3.33 ((~((~((~aSet0(slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), slbdtsldtrb0(xS, xk))))) | (~((~(slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk))))))))))) <=> (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))))),
% 3.15/3.33 inference(rewrite,[status(thm)],[])).
% 3.15/3.33 tff(93,plain,
% 3.15/3.33 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), slbdtsldtrb0(xS, xk))))) | (~((~(slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk))))))))),
% 3.15/3.33 inference(monotonicity,[status(thm)],[92])).
% 3.15/3.33 tff(94,plain,
% 3.15/3.33 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), slbdtsldtrb0(xS, xk))))) | (~((~(slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk))))))))),
% 3.15/3.34 inference(transitivity,[status(thm)],[93, 91])).
% 3.15/3.34 tff(95,plain,
% 3.15/3.34 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(slbdtsldtrb0(xS, xk), xk, xS), slbdtsldtrb0(xS, xk))))) | (~((~(slbdtsldtrb0(xS, xk) = slbdtsldtrb0(xS, xk))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))))))))),
% 3.15/3.34 inference(quant_inst,[status(thm)],[])).
% 3.15/3.34 tff(96,plain,
% 3.15/3.34 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = slbdtsldtrb0(xS, xk)) | (((~aSubsetOf0(tptp_fun_W3_10(W2, xk, xS), xS)) | (~(sbrdtbr0(tptp_fun_W3_10(W2, xk, xS)) = xk))) <=> aElementOf0(tptp_fun_W3_10(W2, xk, xS), W2)))) | (~((~(W2 = slbdtsldtrb0(xS, xk))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(slbdtsldtrb0(xS, xk))) | (~![W3: $i] : (~(((~aSubsetOf0(W3, xS)) | (~(sbrdtbr0(W3) = xk))) <=> aElementOf0(W3, slbdtsldtrb0(xS, xk)))))))),
% 3.15/3.34 inference(modus_ponens,[status(thm)],[95, 94])).
% 3.15/3.34 tff(97,plain,
% 3.15/3.34 ($false),
% 3.15/3.34 inference(unit_resolution,[status(thm)],[96, 90, 49])).
% 3.15/3.34 % SZS output end Proof
% 3.15/3.35 % E exiting
%------------------------------------------------------------------------------