%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN365+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:54 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN365+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:36:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_p_type, type, (
% 0.11/0.36 big_p: $i > $o)).
% 0.11/0.36 tff(h_type, type, (
% 0.11/0.36 h: $i > $i)).
% 0.11/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.11/0.36 tptp_fun_Y_0: $i > $i)).
% 0.11/0.36 tff(tptp_fun_X_1_type, type, (
% 0.11/0.36 tptp_fun_X_1: $i)).
% 0.11/0.36 tff(g_type, type, (
% 0.11/0.36 g: $i > $i)).
% 0.11/0.36 tff(big_r_type, type, (
% 0.11/0.36 big_r: ( $i * $i ) > $o)).
% 0.11/0.36 tff(1,plain,
% 0.11/0.36 ((big_p(X!1) & ![Y: $i] : (~(big_r(X!1, Y) & big_p(Y)))) <=> (big_p(X!1) & ![Y: $i] : (~(big_r(X!1, Y) & big_p(Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))) <=> (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 ((~((![X: $i] : ?[Y: $i] : (big_p(X) => (big_r(X, g(h(Y))) & big_p(Y))) & ![W: $i] : (big_p(W) => (big_p(g(W)) & big_p(h(W))))) => ![X: $i] : (big_p(X) => ?[Y: $i] : (big_r(X, Y) & big_p(Y))))) <=> (~((~(![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y))) & ![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W)))))) | ![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(4,axiom,(~((![X: $i] : ?[Y: $i] : (big_p(X) => (big_r(X, g(h(Y))) & big_p(Y))) & ![W: $i] : (big_p(W) => (big_p(g(W)) & big_p(h(W))))) => ![X: $i] : (big_p(X) => ?[Y: $i] : (big_r(X, Y) & big_p(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2116')).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 (~((~(![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y))) & ![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W)))))) | ![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.36 tff(6,plain,
% 0.11/0.36 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.11/0.36 inference(or_elim,[status(thm)],[5])).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (big_p(X!1) & ![Y: $i] : (~(big_r(X!1, Y) & big_p(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (big_p(X!1)),
% 0.11/0.36 inference(and_elim,[status(thm)],[10])).
% 0.11/0.36 tff(12,plain,
% 0.11/0.36 (^[X: $i] : refl(((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X)))))) <=> ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X)))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 (^[X: $i] : rewrite(((~big_p(X)) | (big_r(X, g(h(tptp_fun_Y_0(X)))) & big_p(tptp_fun_Y_0(X)))) <=> ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X)))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | (big_r(X, g(h(tptp_fun_Y_0(X)))) & big_p(tptp_fun_Y_0(X)))) <=> ![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.36 tff(16,plain,
% 0.11/0.36 (![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y))) <=> ![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y)))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 (![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y))) & ![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.11/0.36 inference(or_elim,[status(thm)],[5])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[17])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 (![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[18, 16])).
% 0.11/0.36 tff(20,plain,(
% 0.11/0.36 ![X: $i] : ((~big_p(X)) | (big_r(X, g(h(tptp_fun_Y_0(X)))) & big_p(tptp_fun_Y_0(X))))),
% 0.11/0.36 inference(skolemize,[status(sab)],[19])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 (((~![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))) | ((~big_p(X!1)) | (~((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1))))))) <=> ((~![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))) | (~big_p(X!1)) | (~((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))) | ((~big_p(X!1)) | (~((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 ((~![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))) | (~big_p(X!1)) | (~((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 (~((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[25, 22, 11])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1)))) | big_r(X!1, g(h(tptp_fun_Y_0(X!1))))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 (big_r(X!1, g(h(tptp_fun_Y_0(X!1))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 (^[Y: $i] : refl(((~big_p(Y)) | (~big_r(X!1, Y))) <=> ((~big_p(Y)) | (~big_r(X!1, Y))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(30,plain,
% 0.11/0.36 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y))) <=> ![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[29])).
% 0.11/0.36 tff(31,plain,
% 0.11/0.36 (^[Y: $i] : trans(monotonicity(rewrite((big_r(X!1, Y) & big_p(Y)) <=> (~((~big_p(Y)) | (~big_r(X!1, Y))))), ((~(big_r(X!1, Y) & big_p(Y))) <=> (~(~((~big_p(Y)) | (~big_r(X!1, Y))))))), rewrite((~(~((~big_p(Y)) | (~big_r(X!1, Y))))) <=> ((~big_p(Y)) | (~big_r(X!1, Y)))), ((~(big_r(X!1, Y) & big_p(Y))) <=> ((~big_p(Y)) | (~big_r(X!1, Y)))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(32,plain,
% 0.11/0.36 (![Y: $i] : (~(big_r(X!1, Y) & big_p(Y))) <=> ![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.36 tff(33,plain,
% 0.11/0.36 (![Y: $i] : (~(big_r(X!1, Y) & big_p(Y)))),
% 0.11/0.36 inference(and_elim,[status(thm)],[10])).
% 0.11/0.36 tff(34,plain,
% 0.11/0.36 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.36 tff(35,plain,
% 0.11/0.36 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.36 tff(36,plain,
% 0.11/0.36 (((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))) | ((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))))) <=> ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))) | (~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(37,plain,
% 0.11/0.36 ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))) | ((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(38,plain,
% 0.11/0.36 ((~![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))) | (~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_r(X!1, g(h(tptp_fun_Y_0(X!1)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.36 tff(39,plain,
% 0.11/0.36 (~big_p(g(h(tptp_fun_Y_0(X!1))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[38, 35, 28])).
% 0.11/0.36 tff(40,plain,
% 0.11/0.36 (((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1)))))) | big_p(g(h(tptp_fun_Y_0(X!1))))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 ((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1)))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (^[W: $i] : refl(((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W)))))) <=> ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W)))))) <=> ![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[42])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (^[W: $i] : rewrite(((~big_p(W)) | (big_p(g(W)) & big_p(h(W)))) <=> ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W)))) <=> ![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W)))) <=> ![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.11/0.37 inference(and_elim,[status(thm)],[17])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.11/0.37 tff(49,plain,(
% 0.11/0.37 ![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[48])).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | ((~big_p(h(tptp_fun_Y_0(X!1)))) | (~((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1))))))))) <=> ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | (~big_p(h(tptp_fun_Y_0(X!1)))) | (~((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1))))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | ((~big_p(h(tptp_fun_Y_0(X!1)))) | (~((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1))))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | (~big_p(h(tptp_fun_Y_0(X!1)))) | (~((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1)))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (~big_p(h(tptp_fun_Y_0(X!1)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[54, 51, 41])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1))))) | big_p(h(tptp_fun_Y_0(X!1)))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 ((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1)))) | big_p(tptp_fun_Y_0(X!1))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 (big_p(tptp_fun_Y_0(X!1))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[58, 26])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | ((~big_p(tptp_fun_Y_0(X!1))) | (~((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1)))))))) <=> ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | (~big_p(tptp_fun_Y_0(X!1))) | (~((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1)))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | ((~big_p(tptp_fun_Y_0(X!1))) | (~((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1)))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | (~big_p(tptp_fun_Y_0(X!1))) | (~((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[62, 51, 59, 57])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------