%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM547+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM547+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 : Fri Jun 20 01:26:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(aElementOf0_type, type, (
% 0.20/0.41 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.41 tff(xS_type, type, (
% 0.20/0.41 xS: $i)).
% 0.20/0.41 tff(tptp_fun_W1_11_type, type, (
% 0.20/0.41 tptp_fun_W1_11: $i > $i)).
% 0.20/0.41 tff(tptp_fun_W0_13_type, type, (
% 0.20/0.41 tptp_fun_W0_13: $i)).
% 0.20/0.41 tff(aSet0_type, type, (
% 0.20/0.41 aSet0: $i > $o)).
% 0.20/0.41 tff(aSubsetOf0_type, type, (
% 0.20/0.41 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.41 tff(xk_type, type, (
% 0.20/0.41 xk: $i)).
% 0.20/0.41 tff(sbrdtbr0_type, type, (
% 0.20/0.41 sbrdtbr0: $i > $i)).
% 0.20/0.41 tff(slbdtsldtrb0_type, type, (
% 0.20/0.41 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.20/0.41 tff(slcrc0_type, type, (
% 0.20/0.41 slcrc0: $i)).
% 0.20/0.41 tff(xT_type, type, (
% 0.20/0.41 xT: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk)) <=> ?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~(![W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(xS, xk)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, slbdtsldtrb0(xS, xk)))) => ((~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slcrc0)))) <=> (~((~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slcrc0) | (~![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(xS, xk)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,axiom,((((((aSet0(slbdtsldtrb0(xS, xk)) & ![W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(xS, xk)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, slbdtsldtrb0(xS, xk))))) & aSet0(slbdtsldtrb0(xT, xk))) & ![W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(xT, xk)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xT))) & aSubsetOf0(W0, xT)) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xT))) | aSubsetOf0(W0, xT)) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, slbdtsldtrb0(xT, xk))))) & ![W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) => aElementOf0(W0, slbdtsldtrb0(xT, xk)))) & aSubsetOf0(slbdtsldtrb0(xS, xk), slbdtsldtrb0(xT, xk))) & (~(![W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(xS, xk)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, slbdtsldtrb0(xS, xk)))) => ((~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slcrc0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2227')).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (~(![W0: $i] : ((aElementOf0(W0, slbdtsldtrb0(xS, xk)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, slbdtsldtrb0(xS, xk)))) => ((~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slcrc0)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[3])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~((~?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (slbdtsldtrb0(xS, xk) = slcrc0) | (~![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(xS, xk))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 2])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 0.20/0.42 inference(or_elim,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(xS, xk))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.20/0.42 tff(8,plain,(
% 0.20/0.42 aElementOf0(W0!13, slbdtsldtrb0(xS, xk))),
% 0.20/0.42 inference(skolemize,[status(sab)],[7])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((aElementOf0(W0!13, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0!13) = xk)) | (~(aSubsetOf0(W0!13, xS) | (~((~aSet0(W0!13)) | (~((~aElementOf0(tptp_fun_W1_11(W0!13), W0!13)) | aElementOf0(tptp_fun_W1_11(W0!13), xS)))))))))) | (~aElementOf0(W0!13, slbdtsldtrb0(xS, xk)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (aElementOf0(W0!13, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0!13) = xk)) | (~(aSubsetOf0(W0!13, xS) | (~((~aSet0(W0!13)) | (~((~aElementOf0(tptp_fun_W1_11(W0!13), W0!13)) | aElementOf0(tptp_fun_W1_11(W0!13), xS)))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (^[W0: $i] : refl((~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))))))) <=> (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (![W0: $i] : (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))))))) <=> ![W0: $i] : (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) <=> (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))), ((((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk))) <=> ((~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))) | (~(sbrdtbr0(W0) = xk))))), rewrite(((~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))) | (~(sbrdtbr0(W0) = xk))) <=> ((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))))), ((((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk))) <=> ((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))), (((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & (((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk)))) <=> ((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & ((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))))))), rewrite(((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & ((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))))) <=> (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))), (((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & (((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk)))) <=> (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![W0: $i] : ((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & (((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk)))) <=> ![W0: $i] : (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk)))) <=> (~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 ((~?[W0: $i] : ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk)) | aElementOf0(W0, slbdtsldtrb0(xS, xk)))) <=> (~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(17,axiom,(~?[W0: $i] : ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xk)) | aElementOf0(W0, slbdtsldtrb0(xS, xk)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (~?[W0: $i] : (aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (^[W0: $i] : nnf_neg(refl($oeq((~aElementOf0(W0, slbdtsldtrb0(xS, xk))), (~aElementOf0(W0, slbdtsldtrb0(xS, xk))))), nnf_neg(nnf_neg(refl($oeq((~aSubsetOf0(W0, xS)), (~aSubsetOf0(W0, xS)))), nnf_neg(refl($oeq((~aSet0(W0)), (~aSet0(W0)))), sk($oeq((~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))), (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))), $oeq((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))), ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))), $oeq((~(aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS))))), ((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))))), refl($oeq((~(sbrdtbr0(W0) = xk)), (~(sbrdtbr0(W0) = xk)))), $oeq((~((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk))), (((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk))))), $oeq((~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | ((aSubsetOf0(W0, xS) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)))) & (sbrdtbr0(W0) = xk)))), ((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & (((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(23,plain,(
% 0.20/0.43 ![W0: $i] : ((~aElementOf0(W0, slbdtsldtrb0(xS, xk))) & (((~aSubsetOf0(W0, xS)) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS))))) | (~(sbrdtbr0(W0) = xk))))),
% 0.20/0.43 inference(nnf-neg,[status(sab)],[21, 22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![W0: $i] : (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 14])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (![W0: $i] : (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[24, 12])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~![W0: $i] : (~(aElementOf0(W0, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, xS) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), xS)))))))))))) | (~(aElementOf0(W0!13, slbdtsldtrb0(xS, xk)) | (~((~(sbrdtbr0(W0!13) = xk)) | (~(aSubsetOf0(W0!13, xS) | (~((~aSet0(W0!13)) | (~((~aElementOf0(tptp_fun_W1_11(W0!13), W0!13)) | aElementOf0(tptp_fun_W1_11(W0!13), xS)))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[26, 25, 10])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------