TSTP Solution File: SYN365+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN365+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Thu Sep 29 23:54:59 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN365+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.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 : Mon Sep 5 02:51:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(big_p_type, type, (
% 0.20/0.41 big_p: $i > $o)).
% 0.20/0.41 tff(h_type, type, (
% 0.20/0.41 h: $i > $i)).
% 0.20/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.41 tptp_fun_Y_0: $i > $i)).
% 0.20/0.41 tff(tptp_fun_X_1_type, type, (
% 0.20/0.41 tptp_fun_X_1: $i)).
% 0.20/0.41 tff(g_type, type, (
% 0.20/0.41 g: $i > $i)).
% 0.20/0.41 tff(big_r_type, type, (
% 0.20/0.41 big_r: ( $i * $i ) > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (((~(~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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![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))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((~((![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)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 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/sandbox2/benchmark/theBenchmark.p','x2116')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~((~(![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))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[5])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (~![X: $i] : ((~big_p(X)) | ?[Y: $i] : (big_r(X, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (big_p(X!1) & ![Y: $i] : (~(big_r(X!1, Y) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (big_p(X!1)),
% 0.20/0.41 inference(and_elim,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (^[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)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (![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))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (^[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)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![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))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (![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)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![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))))),
% 0.20/0.41 inference(or_elim,[status(thm)],[5])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![X: $i] : ?[Y: $i] : ((~big_p(X)) | (big_r(X, g(h(Y))) & big_p(Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 19])).
% 0.20/0.41 tff(23,plain,(
% 0.20/0.41 ![X: $i] : ((~big_p(X)) | (big_r(X, g(h(tptp_fun_Y_0(X)))) & big_p(tptp_fun_Y_0(X))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![X: $i] : ((~big_p(X)) | (~((~big_r(X, g(h(tptp_fun_Y_0(X))))) | (~big_p(tptp_fun_Y_0(X))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 16])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![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))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![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))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~![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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~((~big_r(X!1, g(h(tptp_fun_Y_0(X!1))))) | (~big_p(tptp_fun_Y_0(X!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[28, 25, 14])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (((~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))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (big_r(X!1, g(h(tptp_fun_Y_0(X!1))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (^[Y: $i] : refl(((~big_p(Y)) | (~big_r(X!1, Y))) <=> ((~big_p(Y)) | (~big_r(X!1, Y))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y))) <=> ![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (^[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)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (![Y: $i] : (~(big_r(X!1, Y) & big_p(Y))) <=> ![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![Y: $i] : (~(big_r(X!1, Y) & big_p(Y)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[13])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![Y: $i] : ((~big_p(Y)) | (~big_r(X!1, Y)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![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))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~![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))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (~big_p(g(h(tptp_fun_Y_0(X!1))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~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))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~big_p(g(h(tptp_fun_Y_0(X!1))))) | (~big_p(h(h(tptp_fun_Y_0(X!1)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (^[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)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![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))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (^[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)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![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))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.20/0.42 inference(and_elim,[status(thm)],[20])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.42 tff(52,plain,(
% 0.20/0.42 ![W: $i] : ((~big_p(W)) | (big_p(g(W)) & big_p(h(W))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~![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))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~![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))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 ((~![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)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (~big_p(h(tptp_fun_Y_0(X!1)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[57, 54, 44])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~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)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 ((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~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))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (big_p(tptp_fun_Y_0(X!1))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 29])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~![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)))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~![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)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 ((~![W: $i] : ((~big_p(W)) | (~((~big_p(g(W))) | (~big_p(h(W))))))) | (~big_p(tptp_fun_Y_0(X!1))) | (~((~big_p(g(tptp_fun_Y_0(X!1)))) | (~big_p(h(tptp_fun_Y_0(X!1))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[65, 54, 62, 60])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------