TSTP Solution File: SYN728+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN728+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:57:07 EDT 2022
% Result : Theorem 2.99s 2.23s
% Output : Proof 3.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN728+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n023.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 07:08:47 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.
% 2.99/2.23 % SZS status Theorem
% 2.99/2.23 % SZS output start Proof
% 2.99/2.23 tff(p_type, type, (
% 2.99/2.23 p: ( $i * $i ) > $o)).
% 2.99/2.23 tff(tptp_fun_S_0_type, type, (
% 2.99/2.23 tptp_fun_S_0: $i > $i)).
% 2.99/2.23 tff(g_type, type, (
% 2.99/2.23 g: $i > $i)).
% 2.99/2.23 tff(f_type, type, (
% 2.99/2.23 f: ( $i * $i ) > $i)).
% 2.99/2.23 tff(elem_2_type, type, (
% 2.99/2.23 elem_2: $i)).
% 2.99/2.23 tff(tptp_fun_U_1_type, type, (
% 2.99/2.23 tptp_fun_U_1: $i)).
% 2.99/2.23 tff(q_type, type, (
% 2.99/2.23 q: $i > $o)).
% 2.99/2.23 tff(m_type, type, (
% 2.99/2.23 m: $i > $o)).
% 2.99/2.23 tff(1,assumption,(~p(U!1, U!1)), introduced(assumption)).
% 2.99/2.23 tff(2,assumption,(p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))), introduced(assumption)).
% 2.99/2.23 tff(3,plain,
% 2.99/2.23 (^[X: $i, Z: $i, Y: $i] : refl(((~p(X, Y)) | p(Z, Z)) <=> ((~p(X, Y)) | p(Z, Z)))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(4,plain,
% 2.99/2.23 (![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[3])).
% 2.99/2.23 tff(5,plain,
% 2.99/2.23 (![X: $i] : ![Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(pull_quant,[status(thm)],[])).
% 2.99/2.23 tff(6,plain,
% 2.99/2.23 (^[X: $i] : pull_quant((![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z)))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(7,plain,
% 2.99/2.23 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i] : ![Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[6])).
% 2.99/2.23 tff(8,plain,
% 2.99/2.23 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(transitivity,[status(thm)],[7, 5])).
% 2.99/2.23 tff(9,plain,
% 2.99/2.23 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(transitivity,[status(thm)],[8, 4])).
% 2.99/2.23 tff(10,plain,
% 2.99/2.23 (^[X: $i] : rewrite((![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(11,plain,
% 2.99/2.23 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[10])).
% 2.99/2.23 tff(12,plain,
% 2.99/2.23 (![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(transitivity,[status(thm)],[11, 9])).
% 2.99/2.23 tff(13,plain,
% 2.99/2.23 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) <=> ![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(14,plain,
% 2.99/2.23 ((~(((![X: $i] : (?[Y: $i] : p(X, Y) => ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))) & ![W: $i] : (q(W) => (~m(g(W))))) => ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))) <=> (~((~(![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) & ![W: $i] : ((~q(W)) | (~m(g(W)))))) | ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(15,axiom,(~(((![X: $i] : (?[Y: $i] : p(X, Y) => ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))) & ![W: $i] : (q(W) => (~m(g(W))))) => ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm69')).
% 2.99/2.23 tff(16,plain,
% 2.99/2.23 (~((~(![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) & ![W: $i] : ((~q(W)) | (~m(g(W)))))) | ![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[15, 14])).
% 2.99/2.23 tff(17,plain,
% 2.99/2.23 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z)) & ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) & ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(or_elim,[status(thm)],[16])).
% 2.99/2.23 tff(18,plain,
% 2.99/2.23 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 2.99/2.23 inference(and_elim,[status(thm)],[17])).
% 2.99/2.23 tff(19,plain,
% 2.99/2.23 (![X: $i] : ((~?[Y: $i] : p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[18, 13])).
% 2.99/2.23 tff(20,plain,(
% 2.99/2.23 ![X: $i] : (![Y: $i] : (~p(X, Y)) | ![Z: $i] : p(Z, Z))),
% 2.99/2.23 inference(skolemize,[status(sab)],[19])).
% 2.99/2.23 tff(21,plain,
% 2.99/2.23 (![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[20, 12])).
% 2.99/2.23 tff(22,plain,
% 2.99/2.23 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(23,plain,
% 2.99/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(24,plain,
% 2.99/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(U!1, U!1)),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[23, 22])).
% 2.99/2.23 tff(25,plain,
% 2.99/2.23 ($false),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[24, 21, 2, 1])).
% 2.99/2.23 tff(26,plain,(p(U!1, U!1) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), inference(lemma,lemma(discharge,[]))).
% 2.99/2.23 tff(27,plain,
% 2.99/2.23 (p(U!1, U!1)),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[26, 2])).
% 2.99/2.23 tff(28,assumption,(p(g(U!1), g(U!1))), introduced(assumption)).
% 2.99/2.23 tff(29,assumption,(p(U!1, U!1)), introduced(assumption)).
% 2.99/2.23 tff(30,plain,
% 2.99/2.23 (^[V: $i] : refl(((~p(g(U!1), V)) | (~p(U!1, U!1))) <=> ((~p(g(U!1), V)) | (~p(U!1, U!1))))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(31,plain,
% 2.99/2.23 (![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1))) <=> ![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[30])).
% 2.99/2.23 tff(32,plain,
% 2.99/2.23 (^[V: $i] : trans(monotonicity(rewrite((p(g(U!1), V) & p(U!1, U!1)) <=> (~((~p(g(U!1), V)) | (~p(U!1, U!1))))), ((~(p(g(U!1), V) & p(U!1, U!1))) <=> (~(~((~p(g(U!1), V)) | (~p(U!1, U!1))))))), rewrite((~(~((~p(g(U!1), V)) | (~p(U!1, U!1))))) <=> ((~p(g(U!1), V)) | (~p(U!1, U!1)))), ((~(p(g(U!1), V) & p(U!1, U!1))) <=> ((~p(g(U!1), V)) | (~p(U!1, U!1)))))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(33,plain,
% 2.99/2.23 (![V: $i] : (~(p(g(U!1), V) & p(U!1, U!1))) <=> ![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[32])).
% 2.99/2.23 tff(34,plain,
% 2.99/2.23 ((~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))) <=> (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U)))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(35,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(or_elim,[status(thm)],[16])).
% 2.99/2.23 tff(36,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.99/2.23 tff(37,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[36, 34])).
% 2.99/2.23 tff(38,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[37, 34])).
% 2.99/2.23 tff(39,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.99/2.23 tff(40,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[39, 34])).
% 2.99/2.23 tff(41,plain,
% 2.99/2.23 (~![U: $i] : ?[V: $i] : (p(g(U), V) & p(U, U))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[40, 34])).
% 2.99/2.23 tff(42,plain,(
% 2.99/2.23 $oeq((~?[V: $i] : (p(g(U!1), V) & p(U!1, U!1))), ![V: $i] : (~(p(g(U!1), V) & p(U!1, U!1))))),
% 2.99/2.23 inference(transitivity,[status(sab)],[41])).
% 2.99/2.23 tff(43,plain,
% 2.99/2.23 (![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[42, 33])).
% 2.99/2.23 tff(44,plain,
% 2.99/2.23 (![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[43, 31])).
% 2.99/2.23 tff(45,plain,
% 2.99/2.23 (((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))) <=> ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | (~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(46,plain,
% 2.99/2.23 (((~p(g(U!1), g(U!1))) | (~p(U!1, U!1))) <=> ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(47,plain,
% 2.99/2.23 (((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(g(U!1), g(U!1))) | (~p(U!1, U!1)))) <=> ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(U!1, U!1)) | (~p(g(U!1), g(U!1)))))),
% 2.99/2.23 inference(monotonicity,[status(thm)],[46])).
% 2.99/2.23 tff(48,plain,
% 2.99/2.23 (((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(g(U!1), g(U!1))) | (~p(U!1, U!1)))) <=> ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | (~p(U!1, U!1)) | (~p(g(U!1), g(U!1))))),
% 2.99/2.23 inference(transitivity,[status(thm)],[47, 45])).
% 2.99/2.23 tff(49,plain,
% 2.99/2.23 ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | ((~p(g(U!1), g(U!1))) | (~p(U!1, U!1)))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(50,plain,
% 2.99/2.23 ((~![V: $i] : ((~p(g(U!1), V)) | (~p(U!1, U!1)))) | (~p(U!1, U!1)) | (~p(g(U!1), g(U!1)))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[49, 48])).
% 2.99/2.23 tff(51,plain,
% 2.99/2.23 ($false),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[50, 44, 29, 28])).
% 2.99/2.23 tff(52,plain,((~p(g(U!1), g(U!1))) | (~p(U!1, U!1))), inference(lemma,lemma(discharge,[]))).
% 2.99/2.23 tff(53,plain,
% 2.99/2.23 (~p(g(U!1), g(U!1))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[52, 27])).
% 2.99/2.23 tff(54,plain,
% 2.99/2.23 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(g(U!1), g(U!1)))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(g(U!1), g(U!1)))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(55,plain,
% 2.99/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(g(U!1), g(U!1)))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(56,plain,
% 2.99/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(g(U!1), g(U!1))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.99/2.23 tff(57,plain,
% 2.99/2.23 ($false),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[56, 21, 2, 53])).
% 2.99/2.23 tff(58,plain,(~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))), inference(lemma,lemma(discharge,[]))).
% 2.99/2.23 tff(59,assumption,((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))), introduced(assumption)).
% 2.99/2.23 tff(60,assumption,(~p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))), introduced(assumption)).
% 2.99/2.23 tff(61,plain,
% 2.99/2.23 (^[R: $i] : refl((p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(62,plain,
% 2.99/2.23 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))) <=> ![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[61])).
% 2.99/2.23 tff(63,plain,
% 2.99/2.23 (^[R: $i] : trans(monotonicity(rewrite((m(R) & q(f(R, tptp_fun_S_0(R)))) <=> (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))), ((p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))))), rewrite((p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R))))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))), ((p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R))))) <=> (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(64,plain,
% 2.99/2.23 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R))))) <=> ![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[63])).
% 2.99/2.23 tff(65,plain,
% 2.99/2.23 (![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S)))) <=> ![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(66,plain,
% 2.99/2.23 (![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))),
% 2.99/2.23 inference(and_elim,[status(thm)],[17])).
% 2.99/2.23 tff(67,plain,
% 2.99/2.23 (![R: $i] : ?[S: $i] : (p(R, S) | (m(R) & q(f(R, S))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[66, 65])).
% 2.99/2.23 tff(68,plain,(
% 2.99/2.23 ![R: $i] : (p(R, tptp_fun_S_0(R)) | (m(R) & q(f(R, tptp_fun_S_0(R)))))),
% 2.99/2.23 inference(skolemize,[status(sab)],[67])).
% 2.99/2.23 tff(69,plain,
% 2.99/2.23 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[68, 64])).
% 2.99/2.23 tff(70,plain,
% 2.99/2.23 (![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[69, 62])).
% 2.99/2.23 tff(71,plain,
% 2.99/2.23 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(72,plain,
% 2.99/2.23 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(73,plain,
% 2.99/2.23 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[72, 71])).
% 2.99/2.23 tff(74,plain,
% 2.99/2.23 ($false),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[73, 70, 60, 59])).
% 2.99/2.23 tff(75,plain,((~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))) | p(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))), inference(lemma,lemma(discharge,[]))).
% 2.99/2.23 tff(76,plain,
% 2.99/2.23 (~((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[75, 58])).
% 2.99/2.23 tff(77,plain,
% 2.99/2.23 (((~m(g(f(elem!2, tptp_fun_S_0(elem!2))))) | (~q(f(g(f(elem!2, tptp_fun_S_0(elem!2))), tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))) | m(g(f(elem!2, tptp_fun_S_0(elem!2))))),
% 2.99/2.23 inference(tautology,[status(thm)],[])).
% 2.99/2.23 tff(78,plain,
% 2.99/2.23 (m(g(f(elem!2, tptp_fun_S_0(elem!2))))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[77, 76])).
% 2.99/2.23 tff(79,plain,
% 2.99/2.23 (^[W: $i] : refl(((~q(W)) | (~m(g(W)))) <=> ((~q(W)) | (~m(g(W)))))),
% 2.99/2.23 inference(bind,[status(th)],[])).
% 2.99/2.23 tff(80,plain,
% 2.99/2.23 (![W: $i] : ((~q(W)) | (~m(g(W)))) <=> ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(quant_intro,[status(thm)],[79])).
% 2.99/2.23 tff(81,plain,
% 2.99/2.23 (![W: $i] : ((~q(W)) | (~m(g(W)))) <=> ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(82,plain,
% 2.99/2.23 (![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(and_elim,[status(thm)],[17])).
% 2.99/2.23 tff(83,plain,
% 2.99/2.23 (![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.99/2.23 tff(84,plain,(
% 2.99/2.23 ![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(skolemize,[status(sab)],[83])).
% 2.99/2.23 tff(85,plain,
% 2.99/2.23 (![W: $i] : ((~q(W)) | (~m(g(W))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.99/2.23 tff(86,plain,
% 2.99/2.23 (((~![W: $i] : ((~q(W)) | (~m(g(W))))) | ((~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))))) <=> ((~![W: $i] : ((~q(W)) | (~m(g(W))))) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(87,plain,
% 2.99/2.23 ((~![W: $i] : ((~q(W)) | (~m(g(W))))) | ((~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2))))))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(88,plain,
% 2.99/2.23 ((~![W: $i] : ((~q(W)) | (~m(g(W))))) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2)))))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.99/2.23 tff(89,plain,
% 2.99/2.23 ((~q(f(elem!2, tptp_fun_S_0(elem!2)))) | (~m(g(f(elem!2, tptp_fun_S_0(elem!2)))))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[88, 85])).
% 2.99/2.23 tff(90,plain,
% 2.99/2.23 (~q(f(elem!2, tptp_fun_S_0(elem!2)))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[89, 78])).
% 2.99/2.23 tff(91,plain,
% 2.99/2.23 (((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2))))) | q(f(elem!2, tptp_fun_S_0(elem!2)))),
% 2.99/2.23 inference(tautology,[status(thm)],[])).
% 2.99/2.23 tff(92,plain,
% 2.99/2.23 ((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2))))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[91, 90])).
% 2.99/2.23 tff(93,plain,
% 2.99/2.23 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(94,plain,
% 2.99/2.23 ((p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2))))))) <=> ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(95,plain,
% 2.99/2.23 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2))))),
% 2.99/2.23 inference(monotonicity,[status(thm)],[94])).
% 2.99/2.23 tff(96,plain,
% 2.99/2.23 (((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))))) <=> ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2)))),
% 2.99/2.23 inference(transitivity,[status(thm)],[95, 93])).
% 2.99/2.23 tff(97,plain,
% 2.99/2.23 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (p(elem!2, tptp_fun_S_0(elem!2)) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(98,plain,
% 2.99/2.23 ((~![R: $i] : (p(R, tptp_fun_S_0(R)) | (~((~m(R)) | (~q(f(R, tptp_fun_S_0(R)))))))) | (~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2))),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[97, 96])).
% 2.99/2.23 tff(99,plain,
% 2.99/2.23 ((~((~m(elem!2)) | (~q(f(elem!2, tptp_fun_S_0(elem!2)))))) | p(elem!2, tptp_fun_S_0(elem!2))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[98, 70])).
% 2.99/2.23 tff(100,plain,
% 2.99/2.23 (p(elem!2, tptp_fun_S_0(elem!2))),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[99, 92])).
% 2.99/2.23 tff(101,plain,
% 2.99/2.23 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1))),
% 2.99/2.23 inference(rewrite,[status(thm)],[])).
% 2.99/2.23 tff(102,plain,
% 2.99/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1))),
% 2.99/2.23 inference(quant_inst,[status(thm)],[])).
% 2.99/2.23 tff(103,plain,
% 2.99/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(elem!2, tptp_fun_S_0(elem!2))) | p(U!1, U!1)),
% 2.99/2.23 inference(modus_ponens,[status(thm)],[102, 101])).
% 2.99/2.23 tff(104,plain,
% 2.99/2.23 ($false),
% 2.99/2.23 inference(unit_resolution,[status(thm)],[103, 21, 100, 1])).
% 3.12/2.23 tff(105,plain,(p(U!1, U!1)), inference(lemma,lemma(discharge,[]))).
% 3.12/2.23 tff(106,plain,
% 3.12/2.23 (~p(g(U!1), g(U!1))),
% 3.12/2.23 inference(unit_resolution,[status(thm)],[52, 105])).
% 3.12/2.23 tff(107,plain,
% 3.12/2.23 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))))) | p(g(U!1), g(U!1)))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))))) | p(g(U!1), g(U!1)))),
% 3.12/2.23 inference(rewrite,[status(thm)],[])).
% 3.12/2.23 tff(108,plain,
% 3.12/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))))) | p(g(U!1), g(U!1)))),
% 3.12/2.23 inference(quant_inst,[status(thm)],[])).
% 3.12/2.23 tff(109,plain,
% 3.12/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))))) | p(g(U!1), g(U!1))),
% 3.12/2.23 inference(modus_ponens,[status(thm)],[108, 107])).
% 3.12/2.23 tff(110,plain,
% 3.12/2.23 (~p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))))),
% 3.12/2.23 inference(unit_resolution,[status(thm)],[109, 21, 106])).
% 3.12/2.23 tff(111,assumption,(p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))), introduced(assumption)).
% 3.12/2.23 tff(112,plain,
% 3.12/2.23 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))) | p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))))))))))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))) | p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))))))))))),
% 3.12/2.23 inference(rewrite,[status(thm)],[])).
% 3.12/2.23 tff(113,plain,
% 3.12/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))) | p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))))))))))),
% 3.12/2.23 inference(quant_inst,[status(thm)],[])).
% 3.12/2.23 tff(114,plain,
% 3.12/2.23 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))) | p(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))), tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))), tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))))))))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[113, 112])).
% 3.12/2.24 tff(115,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[114, 21, 111, 110])).
% 3.12/2.24 tff(116,plain,(~p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))), inference(lemma,lemma(discharge,[]))).
% 3.12/2.24 tff(117,plain,
% 3.12/2.24 (((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(elem!2, tptp_fun_S_0(elem!2))) | p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))) <=> ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(elem!2, tptp_fun_S_0(elem!2))) | p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))),
% 3.12/2.24 inference(rewrite,[status(thm)],[])).
% 3.12/2.24 tff(118,plain,
% 3.12/2.24 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | ((~p(elem!2, tptp_fun_S_0(elem!2))) | p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))))))))))))),
% 3.12/2.24 inference(quant_inst,[status(thm)],[])).
% 3.12/2.24 tff(119,plain,
% 3.12/2.24 ((~![X: $i, Z: $i, Y: $i] : ((~p(X, Y)) | p(Z, Z))) | (~p(elem!2, tptp_fun_S_0(elem!2))) | p(tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))), tptp_fun_S_0(g(f(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))), tptp_fun_S_0(g(f(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2)))), tptp_fun_S_0(tptp_fun_S_0(g(f(elem!2, tptp_fun_S_0(elem!2))))))))))))),
% 3.12/2.24 inference(modus_ponens,[status(thm)],[118, 117])).
% 3.12/2.24 tff(120,plain,
% 3.12/2.24 ($false),
% 3.12/2.24 inference(unit_resolution,[status(thm)],[119, 21, 100, 116])).
% 3.12/2.24 % SZS output end Proof
%------------------------------------------------------------------------------