%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN068+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:08 AM UTC 2025
% Result : Theorem 0.14s 0.38s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN068+1 : TPTP v9.0.0. Released v2.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n010.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 12:29:27 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.38 % SZS status Theorem
% 0.14/0.38 % SZS output start Proof
% 0.14/0.38 tff(big_g_type, type, (
% 0.14/0.38 big_g: $i > $o)).
% 0.14/0.38 tff(tptp_fun_Y1_1_type, type, (
% 0.14/0.38 tptp_fun_Y1_1: $i > $i)).
% 0.14/0.38 tff(tptp_fun_X_2_type, type, (
% 0.14/0.38 tptp_fun_X_2: $i)).
% 0.14/0.38 tff(big_h_type, type, (
% 0.14/0.38 big_h: ( $i * $i ) > $o)).
% 0.14/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.38 tptp_fun_Y_0: $i > $i)).
% 0.14/0.38 tff(big_f_type, type, (
% 0.14/0.38 big_f: $i > $o)).
% 0.14/0.38 tff(big_j_type, type, (
% 0.14/0.38 big_j: $i > $o)).
% 0.14/0.38 tff(1,plain,
% 0.14/0.38 (^[X: $i] : refl((big_f(X) | (~big_j(X))) <=> (big_f(X) | (~big_j(X))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(2,plain,
% 0.14/0.38 (![X: $i] : (big_f(X) | (~big_j(X))) <=> ![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.14/0.38 tff(3,plain,
% 0.14/0.38 (^[X: $i] : trans(monotonicity(rewrite((big_j(X) & (~big_f(X))) <=> (~(big_f(X) | (~big_j(X))))), ((~(big_j(X) & (~big_f(X)))) <=> (~(~(big_f(X) | (~big_j(X))))))), rewrite((~(~(big_f(X) | (~big_j(X))))) <=> (big_f(X) | (~big_j(X)))), ((~(big_j(X) & (~big_f(X)))) <=> (big_f(X) | (~big_j(X)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(4,plain,
% 0.14/0.38 (![X: $i] : (~(big_j(X) & (~big_f(X)))) <=> ![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.38 tff(5,plain,
% 0.14/0.38 ((~?[X: $i] : (big_j(X) & (~big_f(X)))) <=> (~?[X: $i] : (big_j(X) & (~big_f(X))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(6,axiom,(~?[X: $i] : (big_j(X) & (~big_f(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel44')).
% 0.14/0.38 tff(7,plain,
% 0.14/0.38 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.38 tff(8,plain,
% 0.14/0.38 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.14/0.38 tff(9,plain,
% 0.14/0.38 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.14/0.38 tff(10,plain,
% 0.14/0.38 (~?[X: $i] : (big_j(X) & (~big_f(X)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.38 tff(11,plain,
% 0.14/0.38 (^[X: $i] : refl($oeq((~(big_j(X) & (~big_f(X)))), (~(big_j(X) & (~big_f(X))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(12,plain,(
% 0.14/0.38 ![X: $i] : (~(big_j(X) & (~big_f(X))))),
% 0.14/0.38 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.14/0.38 tff(13,plain,
% 0.14/0.38 (![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.14/0.38 tff(14,plain,
% 0.14/0.38 (![X: $i] : (big_f(X) | (~big_j(X)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.14/0.38 tff(15,plain,
% 0.14/0.38 ((big_j(X!2) & ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) <=> (big_j(X!2) & ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(16,plain,
% 0.14/0.38 (?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y))) <=> ?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(17,plain,
% 0.14/0.38 (^[X: $i] : rewrite((big_j(X) & ![Y: $i] : (big_g(Y) => big_h(X, Y))) <=> (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(18,plain,
% 0.14/0.38 (?[X: $i] : (big_j(X) & ![Y: $i] : (big_g(Y) => big_h(X, Y))) <=> ?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.14/0.38 tff(19,axiom,(?[X: $i] : (big_j(X) & ![Y: $i] : (big_g(Y) => big_h(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel44_2')).
% 0.14/0.38 tff(20,plain,
% 0.14/0.38 (?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.38 tff(21,plain,
% 0.14/0.38 (?[X: $i] : (big_j(X) & ![Y: $i] : ((~big_g(Y)) | big_h(X, Y)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.14/0.38 tff(22,plain,
% 0.14/0.38 (big_j(X!2) & ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.14/0.38 tff(23,plain,
% 0.14/0.38 (big_j(X!2)),
% 0.14/0.38 inference(and_elim,[status(thm)],[22])).
% 0.14/0.38 tff(24,plain,
% 0.14/0.38 (((~![X: $i] : (big_f(X) | (~big_j(X)))) | (big_f(X!2) | (~big_j(X!2)))) <=> ((~![X: $i] : (big_f(X) | (~big_j(X)))) | big_f(X!2) | (~big_j(X!2)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(25,plain,
% 0.14/0.38 ((~![X: $i] : (big_f(X) | (~big_j(X)))) | (big_f(X!2) | (~big_j(X!2)))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(26,plain,
% 0.14/0.38 ((~![X: $i] : (big_f(X) | (~big_j(X)))) | big_f(X!2) | (~big_j(X!2))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.14/0.38 tff(27,plain,
% 0.14/0.38 (big_f(X!2)),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[26, 23, 14])).
% 0.14/0.38 tff(28,plain,
% 0.14/0.38 (^[X: $i] : refl(((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))) <=> ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(29,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))) <=> ![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.14/0.38 tff(30,plain,
% 0.14/0.38 (^[X: $i] : rewrite(((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))) <=> ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X)))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(31,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))) <=> ![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.14/0.38 tff(32,plain,
% 0.14/0.38 (^[X: $i] : rewrite(((~big_f(X)) | ((big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X))) & (big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))) <=> ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(33,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | ((big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X))) & (big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))) <=> ![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.14/0.38 tff(34,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(35,plain,
% 0.14/0.38 (^[X: $i] : trans(monotonicity(rewrite((?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))) <=> (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))), ((big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> (big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))))), rewrite((big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))), ((big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(36,plain,
% 0.14/0.38 (![X: $i] : (big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1))))) <=> ![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.14/0.38 tff(37,axiom,(![X: $i] : (big_f(X) => (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel44_1')).
% 0.14/0.38 tff(38,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.38 tff(39,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (?[Y: $i] : (big_g(Y) & big_h(X, Y)) & ?[Y1: $i] : (big_g(Y1) & (~big_h(X, Y1)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.14/0.38 tff(40,plain,(
% 0.14/0.38 ![X: $i] : ((~big_f(X)) | ((big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X))) & (big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X))))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[39])).
% 0.14/0.38 tff(41,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (big_g(tptp_fun_Y_0(X)) & big_h(X, tptp_fun_Y_0(X)) & big_g(tptp_fun_Y1_1(X)) & (~big_h(X, tptp_fun_Y1_1(X)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.14/0.38 tff(42,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.14/0.38 tff(43,plain,
% 0.14/0.38 (![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[42, 29])).
% 0.14/0.38 tff(44,plain,
% 0.14/0.38 (((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | ((~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))))) <=> ((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | (~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(45,plain,
% 0.14/0.38 ((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | ((~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(46,plain,
% 0.14/0.38 ((~![X: $i] : ((~big_f(X)) | (~(big_h(X, tptp_fun_Y1_1(X)) | (~big_g(tptp_fun_Y_0(X))) | (~big_h(X, tptp_fun_Y_0(X))) | (~big_g(tptp_fun_Y1_1(X))))))) | (~big_f(X!2)) | (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.14/0.38 tff(47,plain,
% 0.14/0.38 (~(big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[46, 43, 27])).
% 0.14/0.38 tff(48,plain,
% 0.14/0.38 ((big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2)))) | big_g(tptp_fun_Y1_1(X!2))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(49,plain,
% 0.14/0.38 (big_g(tptp_fun_Y1_1(X!2))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.14/0.38 tff(50,plain,
% 0.14/0.38 ((big_h(X!2, tptp_fun_Y1_1(X!2)) | (~big_g(tptp_fun_Y_0(X!2))) | (~big_h(X!2, tptp_fun_Y_0(X!2))) | (~big_g(tptp_fun_Y1_1(X!2)))) | (~big_h(X!2, tptp_fun_Y1_1(X!2)))),
% 0.14/0.38 inference(tautology,[status(thm)],[])).
% 0.14/0.38 tff(51,plain,
% 0.14/0.38 (~big_h(X!2, tptp_fun_Y1_1(X!2))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.14/0.38 tff(52,plain,
% 0.14/0.38 (^[Y: $i] : refl(((~big_g(Y)) | big_h(X!2, Y)) <=> ((~big_g(Y)) | big_h(X!2, Y)))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(53,plain,
% 0.14/0.38 (![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y)) <=> ![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.14/0.38 tff(54,plain,
% 0.14/0.38 (![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.38 inference(and_elim,[status(thm)],[22])).
% 0.14/0.38 tff(55,plain,
% 0.14/0.38 (![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.14/0.38 tff(56,plain,
% 0.14/0.38 (((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | ((~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2)))) <=> ((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | (~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(57,plain,
% 0.14/0.38 ((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | ((~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2)))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(58,plain,
% 0.14/0.38 ((~![Y: $i] : ((~big_g(Y)) | big_h(X!2, Y))) | (~big_g(tptp_fun_Y1_1(X!2))) | big_h(X!2, tptp_fun_Y1_1(X!2))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.14/0.38 tff(59,plain,
% 0.14/0.38 ($false),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[58, 55, 51, 49])).
% 0.14/0.38 % SZS output end Proof
% 0.14/0.38 % E exiting
%------------------------------------------------------------------------------