%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG104+2 : 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 05:24:13 AM UTC 2025
% Result : Theorem 0.49s 0.69s
% Output : Proof 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : RNG104+2 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:20:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.49/0.69 % SZS status Theorem
% 0.49/0.69 % SZS output start Proof
% 0.49/0.69 tff(aElement0_type, type, (
% 0.49/0.69 aElement0: $i > $o)).
% 0.49/0.69 tff(xx_type, type, (
% 0.49/0.69 xx: $i)).
% 0.49/0.69 tff(sdtasdt0_type, type, (
% 0.49/0.69 sdtasdt0: ( $i * $i ) > $i)).
% 0.49/0.69 tff(tptp_fun_W0_20_type, type, (
% 0.49/0.69 tptp_fun_W0_20: $i)).
% 0.49/0.69 tff(xc_type, type, (
% 0.49/0.69 xc: $i)).
% 0.49/0.69 tff(aElementOf0_type, type, (
% 0.49/0.69 aElementOf0: ( $i * $i ) > $o)).
% 0.49/0.69 tff(slsdtgt0_type, type, (
% 0.49/0.69 slsdtgt0: $i > $i)).
% 0.49/0.69 tff(xy_type, type, (
% 0.49/0.69 xy: $i)).
% 0.49/0.69 tff(xz_type, type, (
% 0.49/0.69 xz: $i)).
% 0.49/0.69 tff(xu_type, type, (
% 0.49/0.69 xu: $i)).
% 0.49/0.69 tff(1,plain,
% 0.49/0.69 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx)) <=> ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(2,axiom,((((?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx)) & aElementOf0(xx, slsdtgt0(xc))) & ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xy))) & aElementOf0(xy, slsdtgt0(xc))) & aElement0(xz)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1933')).
% 0.49/0.69 tff(3,plain,
% 0.49/0.69 (((?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx)) & aElementOf0(xx, slsdtgt0(xc))) & ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xy))) & aElementOf0(xy, slsdtgt0(xc))),
% 0.49/0.69 inference(and_elim,[status(thm)],[2])).
% 0.49/0.69 tff(4,plain,
% 0.49/0.69 ((?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx)) & aElementOf0(xx, slsdtgt0(xc))) & ?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xy))),
% 0.49/0.69 inference(and_elim,[status(thm)],[3])).
% 0.49/0.69 tff(5,plain,
% 0.49/0.69 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx)) & aElementOf0(xx, slsdtgt0(xc))),
% 0.49/0.69 inference(and_elim,[status(thm)],[4])).
% 0.49/0.69 tff(6,plain,
% 0.49/0.69 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx))),
% 0.49/0.69 inference(and_elim,[status(thm)],[5])).
% 0.49/0.69 tff(7,plain,
% 0.49/0.69 (?[W0: $i] : (aElement0(W0) & (sdtasdt0(xc, W0) = xx))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.49/0.69 tff(8,plain,(
% 0.49/0.69 aElement0(W0!20) & (sdtasdt0(xc, W0!20) = xx)),
% 0.49/0.69 inference(skolemize,[status(sab)],[7])).
% 0.49/0.69 tff(9,plain,
% 0.49/0.69 (sdtasdt0(xc, W0!20) = xx),
% 0.49/0.69 inference(and_elim,[status(thm)],[8])).
% 0.49/0.69 tff(10,plain,
% 0.49/0.69 (aElement0(sdtasdt0(xc, W0!20)) <=> aElement0(xx)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[9])).
% 0.49/0.69 tff(11,plain,
% 0.49/0.69 (aElement0(W0!20)),
% 0.49/0.69 inference(and_elim,[status(thm)],[8])).
% 0.49/0.69 tff(12,plain,
% 0.49/0.69 (aElement0(xc) <=> aElement0(xc)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(13,axiom,(aElement0(xc)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1905')).
% 0.49/0.69 tff(14,plain,
% 0.49/0.69 (aElement0(xc)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.49/0.69 tff(15,plain,
% 0.49/0.69 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(16,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[15])).
% 0.49/0.69 tff(17,plain,
% 0.49/0.69 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(18,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[17])).
% 0.49/0.69 tff(19,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(20,plain,
% 0.49/0.69 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(21,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[20])).
% 0.49/0.69 tff(22,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.49/0.69 tff(23,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.49/0.69 tff(24,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.49/0.69 tff(25,plain,(
% 0.49/0.69 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 0.49/0.69 inference(skolemize,[status(sab)],[24])).
% 0.49/0.69 tff(26,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.49/0.69 tff(27,plain,
% 0.49/0.69 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.49/0.69 tff(28,plain,
% 0.49/0.69 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xc, W0!20)) | (~aElement0(W0!20)) | (~aElement0(xc)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xc, W0!20)) | (~aElement0(W0!20)) | (~aElement0(xc)))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(29,plain,
% 0.49/0.69 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xc, W0!20)) | (~aElement0(W0!20)) | (~aElement0(xc)))),
% 0.49/0.69 inference(quant_inst,[status(thm)],[])).
% 0.49/0.69 tff(30,plain,
% 0.49/0.69 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xc, W0!20)) | (~aElement0(W0!20)) | (~aElement0(xc))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.49/0.69 tff(31,plain,
% 0.49/0.69 (aElement0(sdtasdt0(xc, W0!20))),
% 0.49/0.69 inference(unit_resolution,[status(thm)],[30, 27, 14, 11])).
% 0.49/0.69 tff(32,plain,
% 0.49/0.69 (aElement0(xx)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[31, 10])).
% 0.49/0.69 tff(33,plain,
% 0.49/0.69 ((sdtasdt0(xz, xx) = sdtasdt0(xx, xz)) <=> (sdtasdt0(xx, xz) = sdtasdt0(xz, xx))),
% 0.49/0.69 inference(commutativity,[status(thm)],[])).
% 0.49/0.69 tff(34,plain,
% 0.49/0.69 ((sdtasdt0(xc, xu) = xx) <=> (sdtasdt0(xc, xu) = xx)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(35,axiom,(aElement0(xu) & (sdtasdt0(xc, xu) = xx)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1956')).
% 0.49/0.69 tff(36,plain,
% 0.49/0.69 (sdtasdt0(xc, xu) = xx),
% 0.49/0.69 inference(and_elim,[status(thm)],[35])).
% 0.49/0.69 tff(37,plain,
% 0.49/0.69 (sdtasdt0(xc, xu) = xx),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.49/0.69 tff(38,plain,
% 0.49/0.69 (xx = sdtasdt0(xc, xu)),
% 0.49/0.69 inference(symmetry,[status(thm)],[37])).
% 0.49/0.69 tff(39,plain,
% 0.49/0.69 (sdtasdt0(xx, xz) = sdtasdt0(sdtasdt0(xc, xu), xz)),
% 0.49/0.69 inference(monotonicity,[status(thm)],[38])).
% 0.49/0.69 tff(40,plain,
% 0.49/0.69 (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xx, xz)),
% 0.49/0.69 inference(symmetry,[status(thm)],[39])).
% 0.49/0.69 tff(41,plain,
% 0.49/0.69 (aElement0(xu) <=> aElement0(xu)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(42,plain,
% 0.49/0.69 (aElement0(xu)),
% 0.49/0.69 inference(and_elim,[status(thm)],[35])).
% 0.49/0.69 tff(43,plain,
% 0.49/0.69 (aElement0(xu)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.49/0.69 tff(44,plain,
% 0.49/0.69 (aElement0(xz) <=> aElement0(xz)),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(45,plain,
% 0.49/0.69 (aElement0(xz)),
% 0.49/0.69 inference(and_elim,[status(thm)],[2])).
% 0.49/0.69 tff(46,plain,
% 0.49/0.69 (aElement0(xz)),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.49/0.69 tff(47,plain,
% 0.49/0.69 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(48,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[47])).
% 0.49/0.69 tff(49,plain,
% 0.49/0.69 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(50,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[49])).
% 0.49/0.69 tff(51,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(52,plain,
% 0.49/0.69 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aElement0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aElement0(W1) & aElement0(W2))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(53,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[52])).
% 0.49/0.69 tff(54,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 0.49/0.69 tff(55,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.49/0.69 tff(56,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.49/0.69 tff(57,plain,(
% 0.49/0.69 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.49/0.69 inference(skolemize,[status(sab)],[56])).
% 0.49/0.69 tff(58,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.49/0.69 tff(59,plain,
% 0.49/0.69 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.69 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.49/0.69 tff(60,plain,
% 0.49/0.69 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xc)) | (~aElement0(xz)) | (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xc)) | (~aElement0(xz)) | (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(61,plain,
% 0.49/0.69 (((sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))) | (~aElement0(xz)) | (~aElement0(xu)) | (~aElement0(xc))) <=> ((~aElement0(xu)) | (~aElement0(xc)) | (~aElement0(xz)) | (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))))),
% 0.49/0.69 inference(rewrite,[status(thm)],[])).
% 0.49/0.69 tff(62,plain,
% 0.49/0.69 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))) | (~aElement0(xz)) | (~aElement0(xu)) | (~aElement0(xc)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xc)) | (~aElement0(xz)) | (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz)))))),
% 0.49/0.69 inference(monotonicity,[status(thm)],[61])).
% 0.49/0.69 tff(63,plain,
% 0.49/0.69 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))) | (~aElement0(xz)) | (~aElement0(xu)) | (~aElement0(xc)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xc)) | (~aElement0(xz)) | (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))))),
% 0.49/0.69 inference(transitivity,[status(thm)],[62, 60])).
% 0.49/0.69 tff(64,plain,
% 0.49/0.69 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))) | (~aElement0(xz)) | (~aElement0(xu)) | (~aElement0(xc)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(65,plain,
% 0.49/0.70 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xc)) | (~aElement0(xz)) | (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.49/0.70 tff(66,plain,
% 0.49/0.70 (sdtasdt0(sdtasdt0(xc, xu), xz) = sdtasdt0(xc, sdtasdt0(xu, xz))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[65, 59, 14, 46, 43])).
% 0.49/0.70 tff(67,plain,
% 0.49/0.70 (sdtasdt0(xc, sdtasdt0(xu, xz)) = sdtasdt0(sdtasdt0(xc, xu), xz)),
% 0.49/0.70 inference(symmetry,[status(thm)],[66])).
% 0.49/0.70 tff(68,plain,
% 0.49/0.70 (sdtasdt0(xc, sdtasdt0(xu, xz)) = sdtasdt0(xx, xz)),
% 0.49/0.70 inference(transitivity,[status(thm)],[67, 40])).
% 0.49/0.70 tff(69,plain,
% 0.49/0.70 ((sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz))) <=> (sdtasdt0(xz, xx) = sdtasdt0(xx, xz))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[68])).
% 0.49/0.70 tff(70,plain,
% 0.49/0.70 ((sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz))) <=> (sdtasdt0(xx, xz) = sdtasdt0(xz, xx))),
% 0.49/0.70 inference(transitivity,[status(thm)],[69, 33])).
% 0.49/0.70 tff(71,plain,
% 0.49/0.70 ((~(sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz)))) <=> (~(sdtasdt0(xx, xz) = sdtasdt0(xz, xx)))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[70])).
% 0.49/0.70 tff(72,plain,
% 0.49/0.70 ((~(sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz)))) <=> (~(sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz))))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(73,axiom,(~(sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.49/0.70 tff(74,plain,
% 0.49/0.70 (~(sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.49/0.70 tff(75,plain,
% 0.49/0.70 (~(sdtasdt0(xx, xz) = sdtasdt0(xz, xx))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[74, 71])).
% 0.49/0.70 tff(76,plain,
% 0.49/0.70 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(77,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[76])).
% 0.49/0.70 tff(78,plain,
% 0.49/0.70 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), (((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(79,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[78])).
% 0.49/0.70 tff(80,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(81,plain,
% 0.49/0.70 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(82,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[81])).
% 0.49/0.70 tff(83,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 0.49/0.70 tff(84,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.49/0.70 tff(85,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.49/0.70 tff(86,plain,(
% 0.49/0.70 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.49/0.70 inference(skolemize,[status(sab)],[85])).
% 0.49/0.70 tff(87,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.49/0.70 tff(88,plain,
% 0.49/0.70 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.49/0.70 tff(89,plain,
% 0.49/0.70 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xz)) | (~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xz)) | (~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(90,plain,
% 0.49/0.70 (((sdtasdt0(xx, xz) = sdtasdt0(xz, xx)) | (~aElement0(xz)) | (~aElement0(xx))) <=> ((~aElement0(xz)) | (~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(91,plain,
% 0.49/0.70 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xx, xz) = sdtasdt0(xz, xx)) | (~aElement0(xz)) | (~aElement0(xx)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xz)) | (~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[90])).
% 0.49/0.70 tff(92,plain,
% 0.49/0.70 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xx, xz) = sdtasdt0(xz, xx)) | (~aElement0(xz)) | (~aElement0(xx)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xz)) | (~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx)))),
% 0.49/0.70 inference(transitivity,[status(thm)],[91, 89])).
% 0.49/0.70 tff(93,plain,
% 0.49/0.70 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xx, xz) = sdtasdt0(xz, xx)) | (~aElement0(xz)) | (~aElement0(xx)))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(94,plain,
% 0.49/0.70 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xz)) | (~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.49/0.70 tff(95,plain,
% 0.49/0.70 ((~aElement0(xx)) | (sdtasdt0(xx, xz) = sdtasdt0(xz, xx))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[94, 88, 46])).
% 0.49/0.70 tff(96,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[95, 75, 32])).
% 0.49/0.70 % SZS output end Proof
% 0.49/0.70 % E exiting
%------------------------------------------------------------------------------