%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN979+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:41:07 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN979+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.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 : Fri Jun 20 13:02:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_B_0_type, type, (
% 0.12/0.38 tptp_fun_B_0: $i)).
% 0.12/0.38 tff(tptp_fun_A_1_type, type, (
% 0.12/0.38 tptp_fun_A_1: $i)).
% 0.12/0.38 tff(s_type, type, (
% 0.12/0.38 s: $i > $o)).
% 0.12/0.38 tff(r_type, type, (
% 0.12/0.38 r: $i > $o)).
% 0.12/0.38 tff(q_type, type, (
% 0.12/0.38 q: $i > $o)).
% 0.12/0.38 tff(elem_2_type, type, (
% 0.12/0.38 elem_2: $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X: $i, Y: $i] : refl((~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y))))) <=> (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y))))) <=> ![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[X: $i, Y: $i] : rewrite((~((~(((~q(X)) | p(X, A!1)) & q(A!1) & q(B!0) & ((~r(Y)) | p(B!0, Y)) & r(A!1) & r(B!0) & ((~s(A!1)) | p(X, Y)) & s(A!1))) | p(A!1, B!0))) <=> (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![X: $i, Y: $i] : (~((~(((~q(X)) | p(X, A!1)) & q(A!1) & q(B!0) & ((~r(Y)) | p(B!0, Y)) & r(A!1) & r(B!0) & ((~s(A!1)) | p(X, Y)) & s(A!1))) | p(A!1, B!0))) <=> ![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B))) <=> (~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ?[X: $i, Y: $i] : (((((((((q(X) => p(X, A)) & q(A)) & q(B)) & (r(Y) => p(B, Y))) & r(A)) & r(B)) & (s(A) => p(X, Y))) & s(A)) => p(A, B))) <=> (~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,axiom,(~![A: $i, B: $i] : ?[X: $i, Y: $i] : (((((((((q(X) => p(X, A)) & q(A)) & q(B)) & (r(Y) => p(B, Y))) & r(A)) & r(B)) & (s(A) => p(X, Y))) & s(A)) => p(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A)) & q(A) & q(B) & ((~r(Y)) | p(B, Y)) & r(A) & r(B) & ((~s(A)) | p(X, Y)) & s(A))) | p(A, B))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.38 tff(12,plain,(
% 0.12/0.38 $oeq((~?[X: $i, Y: $i] : ((~(((~q(X)) | p(X, A!1)) & q(A!1) & q(B!0) & ((~r(Y)) | p(B!0, Y)) & r(A!1) & r(B!0) & ((~s(A!1)) | p(X, Y)) & s(A!1))) | p(A!1, B!0))), ![X: $i, Y: $i] : (~((~(((~q(X)) | p(X, A!1)) & q(A!1) & q(B!0) & ((~r(Y)) | p(B!0, Y)) & r(A!1) & r(B!0) & ((~s(A!1)) | p(X, Y)) & s(A!1))) | p(A!1, B!0))))),
% 0.12/0.38 inference(transitivity,[status(sab)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2)))))) <=> ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~((~s(A!1)) | p(A!1, B!0) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(elem!2, elem!2))))) <=> (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(elem!2, elem!2)))))) <=> ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(elem!2, elem!2)))))) <=> ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(elem!2, elem!2)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[20, 14])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2)))) | (~p(A!1, B!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (~p(A!1, B!0)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(elem!2)) | p(elem!2, A!1))) | (~((~r(elem!2)) | p(B!0, elem!2))) | (~((~s(A!1)) | p(elem!2, elem!2)))) | s(A!1)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (s(A!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 ((~((~s(A!1)) | p(A!1, B!0))) | (~s(A!1)) | p(A!1, B!0)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (~((~s(A!1)) | p(A!1, B!0))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[26, 25, 23])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0)))) | ((~s(A!1)) | p(A!1, B!0))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0)))))) <=> ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~((~s(A!1)) | p(A!1, B!0) | (~((~q(A!1)) | p(A!1, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(B!0)) | p(B!0, B!0))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(A!1, B!0))))) <=> (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~((~q(A!1)) | p(A!1, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(B!0)) | p(B!0, B!0))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(A!1, B!0)))))) <=> ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~((~q(A!1)) | p(A!1, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(B!0)) | p(B!0, B!0))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(A!1, B!0)))))) <=> ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~((~q(A!1)) | p(A!1, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(B!0)) | p(B!0, B!0))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(A!1, B!0)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~![X: $i, Y: $i] : (~((~s(A!1)) | p(A!1, B!0) | (~((~q(X)) | p(X, A!1))) | (~q(A!1)) | (~q(B!0)) | (~((~r(Y)) | p(B!0, Y))) | (~r(A!1)) | (~r(B!0)) | (~((~s(A!1)) | p(X, Y)))))) | (~((~s(A!1)) | p(A!1, B!0) | (~q(A!1)) | (~q(B!0)) | (~r(A!1)) | (~r(B!0)) | (~((~q(A!1)) | p(A!1, A!1))) | (~((~r(B!0)) | p(B!0, B!0))) | (~((~s(A!1)) | p(A!1, B!0)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 14, 29])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------