TSTP Solution File: SYN943+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN943+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Fri Sep 30 00:01:21 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN943+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 09:38:14 EDT 2022
% 0.12/0.33 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(p_type, type, (
% 0.12/0.39 p: $i > $o)).
% 0.12/0.39 tff(f_type, type, (
% 0.12/0.39 f: $i > $i)).
% 0.12/0.39 tff(tptp_fun_A_0_type, type, (
% 0.12/0.39 tptp_fun_A_0: $i)).
% 0.12/0.39 tff(c_type, type, (
% 0.12/0.39 c: $i > $o)).
% 0.12/0.39 tff(s_type, type, (
% 0.12/0.39 s: ( $i * $i ) > $o)).
% 0.12/0.39 tff(g_type, type, (
% 0.12/0.39 g: $i > $o)).
% 0.12/0.39 tff(e_type, type, (
% 0.12/0.39 e: $i > $o)).
% 0.12/0.39 tff(elem_1_type, type, (
% 0.12/0.39 elem_1: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : refl((~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y)))))) <=> (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y)))))) <=> ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : rewrite((~((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A!0) & e(A!0) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A!0, Y))))))) <=> (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A!0) & e(A!0) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A!0, Y))))))) <=> ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 ((~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))) <=> (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 ((~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (((((p(A) & e(A)) & (e(X) => (g(X) | s(X, f(X))))) & (e(X2) => (g(X2) | c(f(X2))))) & (s(A, Y) => p(Y))) => ((p(X3) & g(X3)) | (p(X4) & c(X4))))) <=> (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(7,axiom,(~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (((((p(A) & e(A)) & (e(X) => (g(X) | s(X, f(X))))) & (e(X2) => (g(X2) | c(f(X2))))) & (s(A, Y) => p(Y))) => ((p(X3) & g(X3)) | (p(X4) & c(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![A: $i] : ?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A) & e(A) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.12/0.39 tff(15,plain,(
% 0.12/0.39 $oeq((~?[X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : ((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A!0) & e(A!0) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A!0, Y))))))), ![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((p(X4) & c(X4)) | (p(X3) & g(X3)) | (~(p(A!0) & e(A!0) & ((~e(X)) | s(X, f(X)) | g(X)) & (c(f(X2)) | g(X2) | (~e(X2))) & (p(Y) | (~s(A!0, Y))))))))),
% 0.12/0.39 inference(transitivity,[status(sab)],[14])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 4])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 2])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~c(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~((~p(f(A!0))) | (~g(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~(g(f(A!0)) | (~e(f(A!0))) | c(f(f(A!0)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~c(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~((~p(f(A!0))) | (~g(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~(g(f(A!0)) | (~e(f(A!0))) | c(f(f(A!0))))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 ((~((~((~p(f(A!0))) | (~g(f(A!0))))) | (~((~p(elem!1)) | (~c(elem!1)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(f(A!0))) | g(f(A!0)) | (~e(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))))) <=> (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~c(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~((~p(f(A!0))) | (~g(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~(g(f(A!0)) | (~e(f(A!0))) | c(f(f(A!0)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~((~p(f(A!0))) | (~g(f(A!0))))) | (~((~p(elem!1)) | (~c(elem!1)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(f(A!0))) | g(f(A!0)) | (~e(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~c(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~((~p(f(A!0))) | (~g(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~(g(f(A!0)) | (~e(f(A!0))) | c(f(f(A!0))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~((~p(f(A!0))) | (~g(f(A!0))))) | (~((~p(elem!1)) | (~c(elem!1)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(f(A!0))) | g(f(A!0)) | (~e(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~c(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~((~p(f(A!0))) | (~g(f(A!0))))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~(g(f(A!0)) | (~e(f(A!0))) | c(f(f(A!0))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[20, 18])).
% 0.12/0.40 tff(22,plain,
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% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
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% 0.12/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[23, 17])).
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% 0.12/0.40 inference(tautology,[status(thm)],[])).
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% 0.12/0.40 (p(f(A!0)) | (~s(A!0, f(A!0)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[25, 24])).
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% 0.12/0.40 inference(rewrite,[status(thm)],[])).
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% 0.12/0.40 inference(rewrite,[status(thm)],[])).
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% 0.12/0.40 inference(monotonicity,[status(thm)],[28])).
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% 0.12/0.40 inference(transitivity,[status(thm)],[29, 27])).
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% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
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% 0.12/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
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% 0.12/0.40 inference(unit_resolution,[status(thm)],[32, 17])).
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% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(35,plain,
% 0.18/0.41 ((~e(A!0)) | s(A!0, f(A!0)) | g(A!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[34, 33])).
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% 0.18/0.41 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~(c(f(elem!1)) | g(elem!1) | (~e(elem!1)))) | (~((~p(A!0)) | (~g(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~(p(A!0) | (~s(A!0, A!0))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~(c(f(elem!1)) | g(elem!1) | (~e(elem!1)))) | (~((~p(A!0)) | (~g(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~(p(A!0) | (~s(A!0, A!0)))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
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% 0.18/0.41 inference(rewrite,[status(thm)],[])).
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% 0.18/0.41 inference(monotonicity,[status(thm)],[37])).
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% 0.18/0.41 inference(transitivity,[status(thm)],[38, 36])).
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% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
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% 0.18/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
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% 0.18/0.41 inference(unit_resolution,[status(thm)],[41, 17])).
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% 0.18/0.41 inference(tautology,[status(thm)],[])).
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% 0.18/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
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% 0.18/0.42 ((~((~c(f(A!0))) | (~p(f(A!0))))) | (~c(f(A!0))) | (~p(f(A!0)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(78,plain,
% 0.18/0.42 (~((~c(f(A!0))) | (~p(f(A!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[77, 76, 64])).
% 0.18/0.42 tff(79,plain,
% 0.18/0.42 (((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0)))))) | ((~c(f(A!0))) | (~p(f(A!0))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(80,plain,
% 0.18/0.42 ((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.18/0.42 tff(81,plain,
% 0.18/0.42 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0))))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(82,plain,
% 0.18/0.42 ((~((~((~p(A!0)) | (~g(A!0)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))))) <=> (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(83,plain,
% 0.18/0.42 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~((~p(A!0)) | (~g(A!0)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0))))))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[82])).
% 0.18/0.43 tff(84,plain,
% 0.18/0.43 (((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~((~p(A!0)) | (~g(A!0)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))))) <=> ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0))))))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[83, 81])).
% 0.18/0.43 tff(85,plain,
% 0.18/0.43 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~((~p(A!0)) | (~g(A!0)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(86,plain,
% 0.18/0.43 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | s(A!0, f(A!0)) | g(A!0))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))) | (~((~c(f(A!0))) | (~p(f(A!0)))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.43 tff(87,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[86, 17, 80])).
% 0.18/0.43 % SZS output end Proof
%------------------------------------------------------------------------------