TSTP Solution File: SYN415+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 23:55:13 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN415+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 03:09:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.34 Usage: tptp [options] [-file:]file
% 0.19/0.34 -h, -? prints this message.
% 0.19/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.34 -m, -model generate model.
% 0.19/0.34 -p, -proof generate proof.
% 0.19/0.34 -c, -core generate unsat core of named formulas.
% 0.19/0.34 -st, -statistics display statistics.
% 0.19/0.34 -t:timeout set timeout (in second).
% 0.19/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.34 -<param>:<value> configuration parameter and value.
% 0.19/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(f_type, type, (
% 0.19/0.39 f: $i > $o)).
% 0.19/0.39 tff(tptp_fun_V_4_type, type, (
% 0.19/0.39 tptp_fun_V_4: $i > $i)).
% 0.19/0.39 tff(tptp_fun_U_3_type, type, (
% 0.19/0.39 tptp_fun_U_3: $i)).
% 0.19/0.39 tff(tptp_fun_X_2_type, type, (
% 0.19/0.39 tptp_fun_X_2: $i)).
% 0.19/0.39 tff(tptp_fun_Z_0_type, type, (
% 0.19/0.39 tptp_fun_Z_0: $i)).
% 0.19/0.39 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.39 tptp_fun_Y_1: $i)).
% 0.19/0.39 tff(1,assumption,(~((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3))) | (~(U!3 = tptp_fun_V_4(U!3)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (~(U!3 = tptp_fun_V_4(U!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3))) | f(tptp_fun_V_4(U!3))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (f(tptp_fun_V_4(U!3))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.19/0.39 tff(6,assumption,(~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))), introduced(assumption)).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y))))) | f(X!2)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (f(X!2)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.19/0.39 tff(9,assumption,(![X: $i] : (~f(X))), introduced(assumption)).
% 0.19/0.39 tff(10,assumption,(f(X!2)), introduced(assumption)).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~![X: $i] : (~f(X))) | (~f(X!2))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[11, 10, 9])).
% 0.19/0.39 tff(13,plain,((~![X: $i] : (~f(X))) | (~f(X!2))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (~![X: $i] : (~f(X))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[13, 8])).
% 0.19/0.39 tff(15,assumption,(~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))), introduced(assumption)).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))) | f(Z!0)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (f(Z!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))) | f(Y!1)),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (f(Y!1)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[18, 15])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))) | (~(Y!1 = Z!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~(Y!1 = Z!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[20, 15])).
% 0.19/0.39 tff(22,assumption,(f(Z!0)), introduced(assumption)).
% 0.19/0.39 tff(23,assumption,(![V: $i] : ((~f(V)) | (U!3 = V))), introduced(assumption)).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (((~![V: $i] : ((~f(V)) | (U!3 = V))) | ((~f(Z!0)) | (U!3 = Z!0))) <=> ((~![V: $i] : ((~f(V)) | (U!3 = V))) | (~f(Z!0)) | (U!3 = Z!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![V: $i] : ((~f(V)) | (U!3 = V))) | ((~f(Z!0)) | (U!3 = Z!0))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~![V: $i] : ((~f(V)) | (U!3 = V))) | (~f(Z!0)) | (U!3 = Z!0)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (U!3 = Z!0),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[26, 23, 22])).
% 0.19/0.39 tff(28,assumption,(f(Y!1)), introduced(assumption)).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (((~![V: $i] : ((~f(V)) | (U!3 = V))) | ((~f(Y!1)) | (U!3 = Y!1))) <=> ((~![V: $i] : ((~f(V)) | (U!3 = V))) | (~f(Y!1)) | (U!3 = Y!1))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~![V: $i] : ((~f(V)) | (U!3 = V))) | ((~f(Y!1)) | (U!3 = Y!1))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~![V: $i] : ((~f(V)) | (U!3 = V))) | (~f(Y!1)) | (U!3 = Y!1)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (U!3 = Y!1),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 23, 28])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (Y!1 = U!3),
% 0.19/0.39 inference(symmetry,[status(thm)],[32])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (Y!1 = Z!0),
% 0.19/0.39 inference(transitivity,[status(thm)],[33, 27])).
% 0.19/0.39 tff(35,assumption,(~(Y!1 = Z!0)), introduced(assumption)).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.39 tff(37,plain,((~![V: $i] : ((~f(V)) | (U!3 = V))) | (Y!1 = Z!0) | (~f(Z!0)) | (~f(Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (~![V: $i] : ((~f(V)) | (U!3 = V))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[37, 21, 17, 19])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))) | ![V: $i] : ((~f(V)) | (U!3 = V))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 ((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))))) <=> ((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))))) <=> ((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 ((f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V))) <=> (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 ((f(X!2) & ![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) <=> (~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (^[Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((f(Y) & f(Z)) <=> (~((~f(Z)) | (~f(Y))))), ((~(f(Y) & f(Z))) <=> (~(~((~f(Z)) | (~f(Y))))))), rewrite((~(~((~f(Z)) | (~f(Y))))) <=> ((~f(Z)) | (~f(Y)))), ((~(f(Y) & f(Z))) <=> ((~f(Z)) | (~f(Y))))), (((~(f(Y) & f(Z))) | (Y = Z)) <=> (((~f(Z)) | (~f(Y))) | (Y = Z)))), rewrite((((~f(Z)) | (~f(Y))) | (Y = Z)) <=> ((Y = Z) | (~f(Z)) | (~f(Y)))), (((~(f(Y) & f(Z))) | (Y = Z)) <=> ((Y = Z) | (~f(Z)) | (~f(Y)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)) <=> ![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) <=> (f(X!2) & ![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) <=> (~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[47, 44])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))) <=> ((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V))))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[48, 43])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))) <=> ((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[49, 42])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 ((((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))) & ((![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0)))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))))) <=> (((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))) & (![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))) <=> ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 ((~((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V))))) <=> ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((f(Y) & f(Z)) => (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : (f(V) => (U = V)))) <=> ((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((f(Y) & f(Z)) => (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : (f(V) => (U = V))))) <=> (~((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.40 tff(56,plain,
% 0.19/0.40 ((~((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((f(Y) & f(Z)) => (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : (f(V) => (U = V))))) <=> ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.40 tff(57,axiom,(~((?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((f(Y) & f(Z)) => (Y = Z))) <=> ?[U: $i] : (f(U) & ![V: $i] : (f(V) => (U = V))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish317')).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.40 tff(59,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[58, 52])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 52])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[61, 52])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 ((~(?[X: $i] : f(X) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z)))) <=> ?[U: $i] : (f(U) & ![V: $i] : ((~f(V)) | (U = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[63, 52])).
% 0.19/0.40 tff(65,plain,(
% 0.19/0.40 ((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))) & ((![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0)))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[64])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 (((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))) & (![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[65, 51])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((f(X!2) & ![Y: $i, Z: $i] : ((~(f(Y) & f(Z))) | (Y = Z))) | (f(U!3) & ![V: $i] : ((~f(V)) | (U!3 = V)))),
% 0.19/0.40 inference(and_elim,[status(thm)],[66])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 ((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 50])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 ((~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))) | (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[68, 41])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (~((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[69, 40])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y))))) | ![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) <=> ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | (Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((Y!1 = Z!0) | (~f(Z!0)) | (~f(Y!1))) <=> ((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((Y!1 = Z!0) | (~f(Z!0)) | (~f(Y!1)))) <=> ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[74])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((Y!1 = Z!0) | (~f(Z!0)) | (~f(Y!1)))) <=> ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | (Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[75, 73])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((Y!1 = Z!0) | (~f(Z!0)) | (~f(Y!1)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | (Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 72, 21, 19, 17])).
% 0.19/0.40 tff(80,plain,((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))) <=> ((~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) | ![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 ((~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) <=> (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))) <=> (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))) <=> ((~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) | ![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))) <=> (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) <=> (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0))) <=> (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) <=> (![X: $i] : (~f(X)) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 ((![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) <=> (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![X: $i] : (~f(X)) | (~((~(f(Y!1) & f(Z!0))) | (Y!1 = Z!0))) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))),
% 0.19/0.40 inference(and_elim,[status(thm)],[66])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U))))) | (~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 85])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 ((~((Y!1 = Z!0) | (~f(Y!1)) | (~f(Z!0)))) | ![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 84])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (![X: $i] : (~f(X)) | ![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[93, 80])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 14])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | ((~f(X!2)) | (~((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))))) <=> ((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | (~f(X!2)) | (~((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | ((~f(X!2)) | (~((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | (~f(X!2)) | (~((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (~((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[98, 8, 95])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2))) | (~(X!2 = tptp_fun_V_4(X!2)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (~(X!2 = tptp_fun_V_4(X!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (((~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2))) | f(tptp_fun_V_4(X!2))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (f(tptp_fun_V_4(X!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[71, 6])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((~f(X!2)) | (~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))) <=> ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | (~f(X!2)) | (~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (((X!2 = tptp_fun_V_4(X!2)) | (~f(tptp_fun_V_4(X!2))) | (~f(X!2))) <=> ((~f(X!2)) | (~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((X!2 = tptp_fun_V_4(X!2)) | (~f(tptp_fun_V_4(X!2))) | (~f(X!2)))) <=> ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((~f(X!2)) | (~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((X!2 = tptp_fun_V_4(X!2)) | (~f(tptp_fun_V_4(X!2))) | (~f(X!2)))) <=> ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | (~f(X!2)) | (~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | ((X!2 = tptp_fun_V_4(X!2)) | (~f(tptp_fun_V_4(X!2))) | (~f(X!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y)))) | (~f(X!2)) | (~f(tptp_fun_V_4(X!2))) | (X!2 = tptp_fun_V_4(X!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 8, 104, 103, 101])).
% 0.19/0.41 tff(112,plain,((~f(X!2)) | (~![Y: $i, Z: $i] : ((Y = Z) | (~f(Z)) | (~f(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (~((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 112])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (![V: $i] : ((~f(V)) | (U!3 = V))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[39, 113])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (((~![V: $i] : ((~f(V)) | (U!3 = V))) | ((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))) <=> ((~![V: $i] : ((~f(V)) | (U!3 = V))) | (~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 ((~![V: $i] : ((~f(V)) | (U!3 = V))) | ((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~![V: $i] : ((~f(V)) | (U!3 = V))) | (~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[117, 114, 5, 3])).
% 0.19/0.41 tff(119,plain,((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(120,assumption,(![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))), introduced(assumption)).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (((~f(U!3)) | (~![V: $i] : ((~f(V)) | (U!3 = V)))) | f(U!3)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (f(U!3)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[121, 113])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | ((~f(U!3)) | (~((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))))) <=> ((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | (~f(U!3)) | (~((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | ((~f(U!3)) | (~((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))) | (~f(U!3)) | (~((~f(tptp_fun_V_4(U!3))) | (U!3 = tptp_fun_V_4(U!3))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 122, 120, 119])).
% 0.19/0.41 tff(127,plain,(~![U: $i] : ((~f(U)) | (~((~f(tptp_fun_V_4(U))) | (U = tptp_fun_V_4(U)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (![X: $i] : (~f(X))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 ((~![X: $i] : (~f(X))) | (~f(U!3))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[129, 122, 128])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------