%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN949+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:41:03 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN949+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:01:22 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(q_type, type, (
% 0.20/0.37 q: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_C_0_type, type, (
% 0.20/0.37 tptp_fun_C_0: $i)).
% 0.20/0.37 tff(tptp_fun_B_1_type, type, (
% 0.20/0.37 tptp_fun_B_1: $i)).
% 0.20/0.37 tff(r_type, type, (
% 0.20/0.37 r: ( $i * $i ) > $o)).
% 0.20/0.37 tff(p_type, type, (
% 0.20/0.37 p: $i > $o)).
% 0.20/0.37 tff(s_type, type, (
% 0.20/0.37 s: $i > $o)).
% 0.20/0.37 tff(tptp_fun_A_2_type, type, (
% 0.20/0.37 tptp_fun_A_2: $i)).
% 0.20/0.37 tff(1,plain,
% 0.20/0.37 (^[X: $i, Y: $i] : refl(((~r(X, Y)) | q(X, Y)) <=> ((~r(X, Y)) | q(X, Y)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) <=> ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))) <=> (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 ((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) <=> (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))) <=> ((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[4])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (((s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))) <=> (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.37 tff(7,plain,
% 0.20/0.37 ((~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))) <=> (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 ((~![A: $i, B: $i, C: $i] : (((((s(A) & s(B)) & r(B, C)) & ![X: $i] : (s(X) => p(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p(X) & q(X, Y)))) <=> (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(9,axiom,(~![A: $i, B: $i, C: $i] : (((((s(A) & s(B)) & r(B, C)) & ![X: $i] : (s(X) => p(X))) & ![X: $i, Y: $i] : (r(X, Y) => q(X, Y))) => ?[X: $i, Y: $i] : (p(X) & q(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 (~![A: $i, B: $i, C: $i] : ((~(s(A) & s(B) & r(B, C) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)))) | ?[X: $i, Y: $i] : (p(X) & q(X, Y)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 (s(A!2) & s(B!1) & r(B!1, C!0) & ![X: $i] : (p(X) | (~s(X))) & ![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y)) & ![X: $i, Y: $i] : (~(p(X) & q(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.20/0.38 inference(and_elim,[status(thm)],[14])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (r(B!1, C!0)),
% 0.20/0.38 inference(and_elim,[status(thm)],[14])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!1, C!0)) | q(B!1, C!0))) <=> ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!1, C!0)) | q(B!1, C!0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | ((~r(B!1, C!0)) | q(B!1, C!0))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~r(X, Y)) | q(X, Y))) | (~r(B!1, C!0)) | q(B!1, C!0)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (q(B!1, C!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[20, 17, 16])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (^[X: $i] : refl((p(X) | (~s(X))) <=> (p(X) | (~s(X))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (![X: $i] : (p(X) | (~s(X))) <=> ![X: $i] : (p(X) | (~s(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![X: $i] : (p(X) | (~s(X)))),
% 0.20/0.38 inference(and_elim,[status(thm)],[14])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (![X: $i] : (p(X) | (~s(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (s(B!1)),
% 0.20/0.38 inference(and_elim,[status(thm)],[14])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~![X: $i] : (p(X) | (~s(X)))) | (p(B!1) | (~s(B!1)))) <=> ((~![X: $i] : (p(X) | (~s(X)))) | p(B!1) | (~s(B!1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 ((~![X: $i] : (p(X) | (~s(X)))) | (p(B!1) | (~s(B!1)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 ((~![X: $i] : (p(X) | (~s(X)))) | p(B!1) | (~s(B!1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (p(B!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 26, 25])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : refl(((~p(X)) | (~q(X, Y))) <=> ((~p(X)) | (~q(X, Y))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y))) <=> ![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (^[X: $i, Y: $i] : trans(monotonicity(rewrite((p(X) & q(X, Y)) <=> (~((~p(X)) | (~q(X, Y))))), ((~(p(X) & q(X, Y))) <=> (~(~((~p(X)) | (~q(X, Y))))))), rewrite((~(~((~p(X)) | (~q(X, Y))))) <=> ((~p(X)) | (~q(X, Y)))), ((~(p(X) & q(X, Y))) <=> ((~p(X)) | (~q(X, Y)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(p(X) & q(X, Y))) <=> ![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (![X: $i, Y: $i] : (~(p(X) & q(X, Y)))),
% 0.20/0.38 inference(and_elim,[status(thm)],[14])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | ((~p(B!1)) | (~q(B!1, C!0)))) <=> ((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | (~p(B!1)) | (~q(B!1, C!0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | ((~p(B!1)) | (~q(B!1, C!0)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~![X: $i, Y: $i] : ((~p(X)) | (~q(X, Y)))) | (~p(B!1)) | (~q(B!1, C!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[40, 37, 30, 21])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.38 % E exiting
%------------------------------------------------------------------------------