%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN328-1 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:38:46 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SYN328-1 : TPTP v9.0.0. Released v1.2.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:32:05 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(h_type, type, (
% 0.19/0.42 h: $i > $o)).
% 0.19/0.42 tff(y_type, type, (
% 0.19/0.42 y: $i > $i)).
% 0.19/0.42 tff(z_type, type, (
% 0.19/0.42 z: $i > $i)).
% 0.19/0.42 tff(elem_0_type, type, (
% 0.19/0.42 elem_0: $i)).
% 0.19/0.42 tff(g_type, type, (
% 0.19/0.42 g: $i > $o)).
% 0.19/0.42 tff(f_type, type, (
% 0.19/0.42 f: $i > $o)).
% 0.19/0.42 tff(1,assumption,(~g(z(y(y(y(y(y(y(y(elem!0)))))))))), introduced(assumption)).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 (^[X: $i] : refl(((~h(y(X))) | g(X)) <=> ((~h(y(X))) | g(X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 (![X: $i] : ((~h(y(X))) | g(X)) <=> ![X: $i] : ((~h(y(X))) | g(X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (![X: $i] : ((~h(y(X))) | g(X)) <=> ![X: $i] : ((~h(y(X))) | g(X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(5,axiom,(![X: $i] : ((~h(y(X))) | g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause6')).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 (![X: $i] : ((~h(y(X))) | g(X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.42 tff(7,plain,(
% 0.19/0.42 ![X: $i] : ((~h(y(X))) | g(X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[6])).
% 0.19/0.42 tff(8,plain,
% 0.19/0.42 (![X: $i] : ((~h(y(X))) | g(X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (((~![X: $i] : ((~h(y(X))) | g(X))) | (g(z(y(y(y(y(y(y(y(elem!0))))))))) | (~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | g(X))) | g(z(y(y(y(y(y(y(y(elem!0))))))))) | (~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (((~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | g(z(y(y(y(y(y(y(y(elem!0)))))))))) <=> (g(z(y(y(y(y(y(y(y(elem!0))))))))) | (~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (((~![X: $i] : ((~h(y(X))) | g(X))) | ((~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | g(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | g(X))) | (g(z(y(y(y(y(y(y(y(elem!0))))))))) | (~h(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (((~![X: $i] : ((~h(y(X))) | g(X))) | ((~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | g(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | g(X))) | g(z(y(y(y(y(y(y(y(elem!0))))))))) | (~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[11, 9])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 ((~![X: $i] : ((~h(y(X))) | g(X))) | ((~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | g(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 ((~![X: $i] : ((~h(y(X))) | g(X))) | g(z(y(y(y(y(y(y(y(elem!0))))))))) | (~h(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (~h(y(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[14, 8, 1])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (^[X: $i] : refl((f(y(X)) | g(X)) <=> (f(y(X)) | g(X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (![X: $i] : (f(y(X)) | g(X)) <=> ![X: $i] : (f(y(X)) | g(X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (![X: $i] : (f(y(X)) | g(X)) <=> ![X: $i] : (f(y(X)) | g(X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(19,axiom,(![X: $i] : (f(y(X)) | g(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 0.19/0.42 tff(20,plain,
% 0.19/0.42 (![X: $i] : (f(y(X)) | g(X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.42 tff(21,plain,(
% 0.19/0.42 ![X: $i] : (f(y(X)) | g(X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[20])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![X: $i] : (f(y(X)) | g(X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (((~![X: $i] : (f(y(X)) | g(X))) | (g(z(y(y(y(y(y(y(y(elem!0))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : (f(y(X)) | g(X))) | g(z(y(y(y(y(y(y(y(elem!0))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 ((f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(z(y(y(y(y(y(y(y(elem!0)))))))))) <=> (g(z(y(y(y(y(y(y(y(elem!0))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (((~![X: $i] : (f(y(X)) | g(X))) | (f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : (f(y(X)) | g(X))) | (g(z(y(y(y(y(y(y(y(elem!0))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[24])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (((~![X: $i] : (f(y(X)) | g(X))) | (f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : (f(y(X)) | g(X))) | g(z(y(y(y(y(y(y(y(elem!0))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[25, 23])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 ((~![X: $i] : (f(y(X)) | g(X))) | (f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 ((~![X: $i] : (f(y(X)) | g(X))) | g(z(y(y(y(y(y(y(y(elem!0))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (f(y(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[28, 22, 1])).
% 0.19/0.42 tff(30,assumption,(~f(z(y(y(y(y(y(y(y(elem!0)))))))))), introduced(assumption)).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (^[X: $i] : refl(((~g(y(X))) | f(X)) <=> ((~g(y(X))) | f(X)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (![X: $i] : ((~g(y(X))) | f(X)) <=> ![X: $i] : ((~g(y(X))) | f(X))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![X: $i] : ((~g(y(X))) | f(X)) <=> ![X: $i] : ((~g(y(X))) | f(X))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(34,axiom,(![X: $i] : ((~g(y(X))) | f(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (![X: $i] : ((~g(y(X))) | f(X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,(
% 0.19/0.42 ![X: $i] : ((~g(y(X))) | f(X))),
% 0.19/0.42 inference(skolemize,[status(sab)],[35])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (![X: $i] : ((~g(y(X))) | f(X))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (((~![X: $i] : ((~g(y(X))) | f(X))) | (f(z(y(y(y(y(y(y(y(elem!0))))))))) | (~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))))) <=> ((~![X: $i] : ((~g(y(X))) | f(X))) | f(z(y(y(y(y(y(y(y(elem!0))))))))) | (~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (((~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | f(z(y(y(y(y(y(y(y(elem!0)))))))))) <=> (f(z(y(y(y(y(y(y(y(elem!0))))))))) | (~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (((~![X: $i] : ((~g(y(X))) | f(X))) | ((~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | f(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : ((~g(y(X))) | f(X))) | (f(z(y(y(y(y(y(y(y(elem!0))))))))) | (~g(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[39])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (((~![X: $i] : ((~g(y(X))) | f(X))) | ((~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | f(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : ((~g(y(X))) | f(X))) | f(z(y(y(y(y(y(y(y(elem!0))))))))) | (~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[40, 38])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 ((~![X: $i] : ((~g(y(X))) | f(X))) | ((~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | f(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 ((~![X: $i] : ((~g(y(X))) | f(X))) | f(z(y(y(y(y(y(y(y(elem!0))))))))) | (~g(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (~g(y(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[43, 37, 30])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (((~![X: $i] : ((~h(y(X))) | g(X))) | (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | g(X))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (((~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (((~![X: $i] : ((~h(y(X))) | g(X))) | ((~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | g(X))) | (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~h(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 (((~![X: $i] : ((~h(y(X))) | g(X))) | ((~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | g(X))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.43 tff(49,plain,
% 0.19/0.43 ((~![X: $i] : ((~h(y(X))) | g(X))) | ((~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 ((~![X: $i] : ((~h(y(X))) | g(X))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~h(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 (~h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[50, 8, 44])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 (^[X: $i] : refl(((~h(y(X))) | h(X)) <=> ((~h(y(X))) | h(X)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 (![X: $i] : ((~h(y(X))) | h(X)) <=> ![X: $i] : ((~h(y(X))) | h(X))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 (![X: $i] : ((~h(y(X))) | h(X)) <=> ![X: $i] : ((~h(y(X))) | h(X))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(55,axiom,(![X: $i] : ((~h(y(X))) | h(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause10')).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (![X: $i] : ((~h(y(X))) | h(X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.43 tff(57,plain,(
% 0.19/0.43 ![X: $i] : ((~h(y(X))) | h(X))),
% 0.19/0.43 inference(skolemize,[status(sab)],[56])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (![X: $i] : ((~h(y(X))) | h(X))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (((~![X: $i] : ((~h(y(X))) | h(X))) | (h(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~h(y(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))))) <=> ((~![X: $i] : ((~h(y(X))) | h(X))) | h(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~h(y(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (((~h(y(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))) | h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> (h(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~h(y(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(61,plain,
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% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(224,plain,
% 0.19/0.45 (((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | h(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (h(z(y(y(y(y(y(y(y(elem!0))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[223])).
% 0.19/0.45 tff(225,plain,
% 0.19/0.45 (((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | h(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | h(z(y(y(y(y(y(y(y(elem!0))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[224, 222])).
% 0.19/0.45 tff(226,plain,
% 0.19/0.45 ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | h(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(227,plain,
% 0.19/0.45 ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | h(z(y(y(y(y(y(y(y(elem!0))))))))) | g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.45 tff(228,plain,
% 0.19/0.45 (g(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[227, 135, 213])).
% 0.19/0.45 tff(229,plain,
% 0.19/0.45 (~f(y(z(y(y(y(y(y(y(y(elem!0))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[228, 221])).
% 0.19/0.45 tff(230,plain,
% 0.19/0.45 (((~![X: $i] : ((~g(y(X))) | f(X))) | (f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))) <=> ((~![X: $i] : ((~g(y(X))) | f(X))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(231,plain,
% 0.19/0.45 (((~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> (f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(232,plain,
% 0.19/0.45 (((~![X: $i] : ((~g(y(X))) | f(X))) | ((~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : ((~g(y(X))) | f(X))) | (f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[231])).
% 0.19/0.45 tff(233,plain,
% 0.19/0.45 (((~![X: $i] : ((~g(y(X))) | f(X))) | ((~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : ((~g(y(X))) | f(X))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[232, 230])).
% 0.19/0.45 tff(234,plain,
% 0.19/0.45 ((~![X: $i] : ((~g(y(X))) | f(X))) | ((~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(235,plain,
% 0.19/0.45 ((~![X: $i] : ((~g(y(X))) | f(X))) | f(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | (~g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.45 tff(236,plain,
% 0.19/0.45 (~g(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[235, 37, 229])).
% 0.19/0.45 tff(237,plain,
% 0.19/0.45 (((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (h(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))) <=> ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | h(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 ((g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | h(y(z(y(y(y(y(y(y(y(elem!0))))))))))) <=> (h(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 (((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | h(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (h(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[238])).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 (((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | h(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) <=> ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | h(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[239, 237])).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | (g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))) | h(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 ((~![X: $i] : (g(y(X)) | (~f(y(X))) | h(X))) | h(y(z(y(y(y(y(y(y(y(elem!0)))))))))) | g(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))) | (~f(y(y(z(y(y(y(y(y(y(y(elem!0))))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.19/0.46 tff(243,plain,
% 0.19/0.46 (~f(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[242, 135, 220, 236])).
% 0.19/0.46 tff(244,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[85, 22, 221, 243])).
% 0.19/0.46 tff(245,plain,(g(y(z(y(y(y(y(y(y(y(elem!0))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 (h(y(y(z(y(y(y(y(y(y(y(elem!0)))))))))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[191, 245])).
% 0.19/0.46 tff(247,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[195, 58, 246, 220])).
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------