%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN954+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:41:04 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN954+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:01:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(q_type, type, (
% 0.18/0.36 q: $i > $o)).
% 0.18/0.36 tff(tptp_fun_A_1_type, type, (
% 0.18/0.36 tptp_fun_A_1: $i)).
% 0.18/0.36 tff(p_type, type, (
% 0.18/0.36 p: $i > $o)).
% 0.18/0.36 tff(tptp_fun_B_0_type, type, (
% 0.18/0.36 tptp_fun_B_0: $i)).
% 0.18/0.36 tff(1,assumption,(~p(B!0)), introduced(assumption)).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (^[Z: $i] : refl((p(Z) | (~q(Z))) <=> (p(Z) | (~q(Z))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (![Z: $i] : (p(Z) | (~q(Z))) <=> ![Z: $i] : (p(Z) | (~q(Z)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 ((![Z: $i] : (p(Z) | (~q(Z))) & ![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))))) <=> (![Z: $i] : (p(Z) | (~q(Z))) & ![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 ((~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))) <=> (~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 ((~![A: $i, B: $i] : (![Z: $i] : (q(Z) => p(Z)) => ?[X: $i] : ((p(X) => p(A)) & (q(X) => p(B))))) <=> (~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X))))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(7,axiom,(~![A: $i, B: $i] : (![Z: $i] : (q(Z) => p(Z)) => ?[X: $i] : ((p(X) => p(A)) & (q(X) => p(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.18/0.36 tff(8,plain,
% 0.18/0.36 (~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.36 tff(11,plain,
% 0.18/0.36 (~![A: $i, B: $i] : ((~![Z: $i] : (p(Z) | (~q(Z)))) | ?[X: $i] : ((p(A) | (~p(X))) & (p(B) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (![Z: $i] : (p(Z) | (~q(Z))) & ![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (![Z: $i] : (p(Z) | (~q(Z)))),
% 0.18/0.36 inference(and_elim,[status(thm)],[12])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 (![Z: $i] : (p(Z) | (~q(Z)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 (((~![Z: $i] : (p(Z) | (~q(Z)))) | (p(B!0) | (~q(B!0)))) <=> ((~![Z: $i] : (p(Z) | (~q(Z)))) | p(B!0) | (~q(B!0)))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(16,plain,
% 0.18/0.36 ((~![Z: $i] : (p(Z) | (~q(Z)))) | (p(B!0) | (~q(B!0)))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(17,plain,
% 0.18/0.36 ((~![Z: $i] : (p(Z) | (~q(Z)))) | p(B!0) | (~q(B!0))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.18/0.36 tff(18,plain,
% 0.18/0.36 (~q(B!0)),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[17, 14, 1])).
% 0.18/0.36 tff(19,plain,
% 0.18/0.36 ((p(B!0) | (~q(B!0))) | q(B!0)),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(20,plain,
% 0.18/0.36 (p(B!0) | (~q(B!0))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.18/0.36 tff(21,plain,
% 0.18/0.36 ((p(A!1) | (~p(B!0))) | p(B!0)),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(22,plain,
% 0.18/0.36 (p(A!1) | (~p(B!0))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[21, 1])).
% 0.18/0.36 tff(23,plain,
% 0.18/0.36 (^[X: $i] : refl(((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))) <=> ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(24,plain,
% 0.18/0.36 (![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))) <=> ![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.36 tff(25,plain,
% 0.18/0.36 (^[X: $i] : trans(monotonicity(rewrite(((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))) <=> (~((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))), ((~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))) <=> (~(~((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))))), rewrite((~(~((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X))))))) <=> ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))), ((~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))) <=> ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(26,plain,
% 0.18/0.36 (![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X))))) <=> ![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.36 tff(27,plain,
% 0.18/0.36 (![X: $i] : (~((p(A!1) | (~p(X))) & (p(B!0) | (~q(X)))))),
% 0.18/0.36 inference(and_elim,[status(thm)],[12])).
% 0.18/0.36 tff(28,plain,
% 0.18/0.36 (![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.36 tff(29,plain,
% 0.18/0.36 (![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.36 tff(30,plain,
% 0.18/0.36 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0)))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(31,plain,
% 0.18/0.36 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0)))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(32,plain,
% 0.18/0.36 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(A!1) | (~p(B!0)))) | (~(p(B!0) | (~q(B!0))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.18/0.36 tff(33,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[32, 29, 22, 20])).
% 0.18/0.36 tff(34,plain,(p(B!0)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.36 tff(35,plain,
% 0.18/0.36 ((p(B!0) | (~q(A!1))) | (~p(B!0))),
% 0.18/0.36 inference(tautology,[status(thm)],[])).
% 0.18/0.36 tff(36,plain,
% 0.18/0.36 (p(B!0) | (~q(A!1))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.18/0.36 tff(37,plain,
% 0.18/0.36 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1)))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(38,plain,
% 0.18/0.36 (($false | (~(p(B!0) | (~q(A!1))))) <=> (~(p(B!0) | (~q(A!1))))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(39,plain,
% 0.18/0.36 ((~$true) <=> $false),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(40,plain,
% 0.18/0.36 ((p(A!1) | (~p(A!1))) <=> $true),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(41,plain,
% 0.18/0.36 ((~(p(A!1) | (~p(A!1)))) <=> (~$true)),
% 0.18/0.36 inference(monotonicity,[status(thm)],[40])).
% 0.18/0.36 tff(42,plain,
% 0.18/0.36 ((~(p(A!1) | (~p(A!1)))) <=> $false),
% 0.18/0.36 inference(transitivity,[status(thm)],[41, 39])).
% 0.18/0.36 tff(43,plain,
% 0.18/0.36 (((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1))))) <=> ($false | (~(p(B!0) | (~q(A!1)))))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[42])).
% 0.18/0.36 tff(44,plain,
% 0.18/0.36 (((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1))))) <=> (~(p(B!0) | (~q(A!1))))),
% 0.18/0.36 inference(transitivity,[status(thm)],[43, 38])).
% 0.18/0.36 tff(45,plain,
% 0.18/0.36 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1)))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1)))))),
% 0.18/0.36 inference(monotonicity,[status(thm)],[44])).
% 0.18/0.36 tff(46,plain,
% 0.18/0.36 (((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1)))))) <=> ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1)))))),
% 0.18/0.36 inference(transitivity,[status(thm)],[45, 37])).
% 0.18/0.36 tff(47,plain,
% 0.18/0.36 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | ((~(p(A!1) | (~p(A!1)))) | (~(p(B!0) | (~q(A!1)))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(48,plain,
% 0.18/0.36 ((~![X: $i] : ((~(p(A!1) | (~p(X)))) | (~(p(B!0) | (~q(X)))))) | (~(p(B!0) | (~q(A!1))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.36 tff(49,plain,
% 0.18/0.36 ($false),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[48, 29, 36])).
% 0.18/0.36 % SZS output end Proof
% 0.18/0.36 % E exiting
%------------------------------------------------------------------------------