%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN943+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:41:02 AM UTC 2025
% Result : Theorem 0.17s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN943+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Fri Jun 20 13:01:57 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.17/0.36 % SZS status Theorem
% 0.17/0.36 % SZS output start Proof
% 0.17/0.36 tff(s_type, type, (
% 0.17/0.36 s: ( $i * $i ) > $o)).
% 0.17/0.36 tff(f_type, type, (
% 0.17/0.36 f: $i > $i)).
% 0.17/0.36 tff(tptp_fun_A_0_type, type, (
% 0.17/0.36 tptp_fun_A_0: $i)).
% 0.17/0.36 tff(p_type, type, (
% 0.17/0.36 p: $i > $o)).
% 0.17/0.36 tff(c_type, type, (
% 0.17/0.36 c: $i > $o)).
% 0.17/0.36 tff(g_type, type, (
% 0.17/0.36 g: $i > $o)).
% 0.17/0.36 tff(e_type, type, (
% 0.17/0.36 e: $i > $o)).
% 0.17/0.36 tff(elem_1_type, type, (
% 0.17/0.36 elem_1: $i)).
% 0.17/0.36 tff(1,plain,
% 0.17/0.36 (^[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)))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(2,plain,
% 0.17/0.36 (![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))))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.36 tff(3,plain,
% 0.17/0.36 (^[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)))))))),
% 0.17/0.36 inference(bind,[status(th)],[])).
% 0.17/0.36 tff(4,plain,
% 0.17/0.36 (![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))))))),
% 0.17/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.36 tff(5,plain,
% 0.17/0.36 ((~![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)))))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(6,plain,
% 0.17/0.36 ((~![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)))))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 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/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.17/0.36 tff(8,plain,
% 0.17/0.36 (~![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))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.17/0.36 tff(9,plain,
% 0.17/0.36 (~![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))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.17/0.36 tff(10,plain,
% 0.17/0.36 (~![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))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.17/0.36 tff(11,plain,
% 0.17/0.36 (~![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))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.17/0.36 tff(12,plain,(
% 0.17/0.36 $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))))))))),
% 0.17/0.36 inference(transitivity,[status(sab)],[11])).
% 0.17/0.36 tff(13,plain,
% 0.17/0.36 (![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))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.17/0.36 tff(14,plain,
% 0.17/0.36 (![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))))))),
% 0.17/0.36 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.17/0.36 tff(15,plain,
% 0.17/0.36 (((~![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)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(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(elem!1)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0))))))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(16,plain,
% 0.17/0.36 ((~((~((~p(elem!1)) | (~g(elem!1)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(elem!1) | (~s(A!0, elem!1)))))) <=> (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0)))))))),
% 0.17/0.36 inference(rewrite,[status(thm)],[])).
% 0.17/0.36 tff(17,plain,
% 0.17/0.36 (((~![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(elem!1)) | (~g(elem!1)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(elem!1) | (~s(A!0, elem!1))))))) <=> ((~![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)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0))))))))),
% 0.17/0.36 inference(monotonicity,[status(thm)],[16])).
% 0.17/0.36 tff(18,plain,
% 0.17/0.36 (((~![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(elem!1)) | (~g(elem!1)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(elem!1) | (~s(A!0, elem!1))))))) <=> ((~![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)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0))))))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[17, 15])).
% 0.17/0.37 tff(19,plain,
% 0.17/0.37 ((~![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(elem!1)) | (~g(elem!1)))) | (~((~p(f(A!0))) | (~c(f(A!0))))) | (~p(A!0)) | (~e(A!0)) | (~((~e(elem!1)) | s(elem!1, f(elem!1)) | g(elem!1))) | (~(c(f(A!0)) | g(A!0) | (~e(A!0)))) | (~(p(elem!1) | (~s(A!0, elem!1))))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(20,plain,
% 0.17/0.37 ((~![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)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0)))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.17/0.37 tff(21,plain,
% 0.17/0.37 (~((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0))))))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[20, 14])).
% 0.17/0.37 tff(22,plain,
% 0.17/0.37 (((~p(A!0)) | (~e(A!0)) | (~((~p(elem!1)) | (~g(elem!1)))) | (~(g(elem!1) | (~e(elem!1)) | s(elem!1, f(elem!1)))) | (~(p(elem!1) | (~s(A!0, elem!1)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~c(f(A!0))) | (~p(f(A!0)))))) | ((~c(f(A!0))) | (~p(f(A!0))))),
% 0.17/0.37 inference(tautology,[status(thm)],[])).
% 0.17/0.37 tff(23,plain,
% 0.17/0.37 ((~c(f(A!0))) | (~p(f(A!0)))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.17/0.37 tff(24,plain,
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% 0.17/0.37 inference(monotonicity,[status(thm)],[25])).
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% 0.17/0.38 inference(tautology,[status(thm)],[])).
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% 0.17/0.38 ((~e(A!0)) | g(A!0) | s(A!0, f(A!0))),
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% 0.17/0.38 inference(tautology,[status(thm)],[])).
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% 0.17/0.38 inference(unit_resolution,[status(thm)],[57, 48])).
% 0.17/0.38 tff(59,plain,
% 0.17/0.38 (s(A!0, f(A!0))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[58, 46, 56])).
% 0.17/0.38 tff(60,plain,
% 0.17/0.38 ((~(p(f(A!0)) | (~s(A!0, f(A!0))))) | p(f(A!0)) | (~s(A!0, f(A!0)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(61,plain,
% 0.17/0.38 (~(p(f(A!0)) | (~s(A!0, f(A!0))))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[60, 59, 54])).
% 0.17/0.38 tff(62,plain,
% 0.17/0.38 (((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))) | (p(f(A!0)) | (~s(A!0, f(A!0))))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(63,plain,
% 0.17/0.38 ((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.17/0.39 tff(64,plain,
% 0.17/0.39 (((~![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(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(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)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
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% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(66,plain,
% 0.17/0.39 (((~![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)) | (~g(A!0)))) | (~((~p(A!0)) | (~c(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)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[65])).
% 0.17/0.39 tff(67,plain,
% 0.17/0.39 (((~![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)) | (~g(A!0)))) | (~((~p(A!0)) | (~c(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)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0))))))))),
% 0.17/0.39 inference(transitivity,[status(thm)],[66, 64])).
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% 0.17/0.39 ((~![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)) | (~g(A!0)))) | (~((~p(A!0)) | (~c(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)))))))),
% 0.17/0.39 inference(quant_inst,[status(thm)],[])).
% 0.17/0.39 tff(69,plain,
% 0.17/0.39 ((~![X: $i, X2: $i, X3: $i, X4: $i, Y: $i] : (~((~((~p(X3)) | (~g(X3)))) | (~((~p(X4)) | (~c(X4)))) | (~p(A!0)) | (~e(A!0)) | (~((~e(X)) | s(X, f(X)) | g(X))) | (~(c(f(X2)) | g(X2) | (~e(X2)))) | (~(p(Y) | (~s(A!0, Y))))))) | (~((~p(A!0)) | (~e(A!0)) | (~((~p(A!0)) | (~g(A!0)))) | (~((~e(A!0)) | g(A!0) | s(A!0, f(A!0)))) | (~((~e(A!0)) | g(A!0) | c(f(A!0)))) | (~((~p(A!0)) | (~c(A!0)))) | (~(p(f(A!0)) | (~s(A!0, f(A!0)))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.17/0.39 tff(70,plain,
% 0.17/0.39 ($false),
% 0.17/0.39 inference(unit_resolution,[status(thm)],[69, 14, 63])).
% 0.17/0.39 % SZS output end Proof
% 0.17/0.39 % E exiting
%------------------------------------------------------------------------------