%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN921+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 05:41:00 AM UTC 2025
% Result : Theorem 0.17s 0.35s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN921+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 13:01:26 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.17/0.35 % SZS status Theorem
% 0.17/0.35 % SZS output start Proof
% 0.17/0.35 tff(p_type, type, (
% 0.17/0.35 p: $i > $o)).
% 0.17/0.35 tff(tptp_fun_Y_0_type, type, (
% 0.17/0.35 tptp_fun_Y_0: $i > $i)).
% 0.17/0.35 tff(elem_1_type, type, (
% 0.17/0.35 elem_1: $i)).
% 0.17/0.35 tff(q_type, type, (
% 0.17/0.35 q: $i > $o)).
% 0.17/0.35 tff(1,plain,
% 0.17/0.35 (^[X: $i] : refl((~((~p(X)) | q(X) | p(tptp_fun_Y_0(X)))) <=> (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X)))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(2,plain,
% 0.17/0.35 (![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X)))) <=> ![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.35 tff(3,plain,
% 0.17/0.35 (^[X: $i] : rewrite((~(q(X) | p(tptp_fun_Y_0(X)) | (~p(X)))) <=> (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X)))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(4,plain,
% 0.17/0.35 (![X: $i] : (~(q(X) | p(tptp_fun_Y_0(X)) | (~p(X)))) <=> ![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))),
% 0.17/0.35 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.35 tff(5,plain,
% 0.17/0.35 ((~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y))) <=> (~?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(6,plain,
% 0.17/0.35 ((~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y)))))) <=> (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y)))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(7,plain,
% 0.17/0.35 ((~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y)))))) <=> (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(8,plain,
% 0.17/0.35 ((~?[X: $i] : ![Y: $i] : ((p(Y) => q(X)) => (p(X) => q(X)))) <=> (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y))))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(9,axiom,(~?[X: $i] : ![Y: $i] : ((p(Y) => q(X)) => (p(X) => q(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_this')).
% 0.17/0.35 tff(10,plain,
% 0.17/0.35 (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.17/0.35 tff(11,plain,
% 0.17/0.35 (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.17/0.35 tff(12,plain,
% 0.17/0.35 (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | (~(q(X) | (~p(Y)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.17/0.35 tff(13,plain,
% 0.17/0.35 (~?[X: $i] : ![Y: $i] : (q(X) | (~p(X)) | p(Y))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.17/0.35 tff(14,plain,
% 0.17/0.35 (~?[X: $i] : ![Y: $i] : (q(X) | p(Y) | (~p(X)))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.17/0.35 tff(15,plain,
% 0.17/0.35 (^[X: $i] : sk($oeq((~![Y: $i] : (q(X) | p(Y) | (~p(X)))), (~(q(X) | p(tptp_fun_Y_0(X)) | (~p(X))))))),
% 0.17/0.35 inference(bind,[status(th)],[])).
% 0.17/0.35 tff(16,plain,(
% 0.17/0.35 ![X: $i] : (~(q(X) | p(tptp_fun_Y_0(X)) | (~p(X))))),
% 0.17/0.35 inference(nnf-neg,[status(sab)],[14, 15])).
% 0.17/0.35 tff(17,plain,
% 0.17/0.35 (![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[16, 4])).
% 0.17/0.35 tff(18,plain,
% 0.17/0.35 (![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[17, 2])).
% 0.17/0.35 tff(19,plain,
% 0.17/0.35 ((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~((~p(elem!1)) | q(elem!1) | p(tptp_fun_Y_0(elem!1))))),
% 0.17/0.35 inference(quant_inst,[status(thm)],[])).
% 0.17/0.35 tff(20,plain,
% 0.17/0.35 (~((~p(elem!1)) | q(elem!1) | p(tptp_fun_Y_0(elem!1)))),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.17/0.35 tff(21,plain,
% 0.17/0.35 (((~p(elem!1)) | q(elem!1) | p(tptp_fun_Y_0(elem!1))) | (~p(tptp_fun_Y_0(elem!1)))),
% 0.17/0.35 inference(tautology,[status(thm)],[])).
% 0.17/0.35 tff(22,plain,
% 0.17/0.35 (~p(tptp_fun_Y_0(elem!1))),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.17/0.35 tff(23,plain,
% 0.17/0.35 ((q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))) | p(tptp_fun_Y_0(elem!1))),
% 0.17/0.35 inference(tautology,[status(thm)],[])).
% 0.17/0.35 tff(24,plain,
% 0.17/0.35 (q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.17/0.35 tff(25,plain,
% 0.17/0.35 (((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~(q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) <=> ((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~(q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(26,plain,
% 0.17/0.35 ((~((~p(tptp_fun_Y_0(elem!1))) | q(tptp_fun_Y_0(elem!1)) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) <=> (~(q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))),
% 0.17/0.35 inference(rewrite,[status(thm)],[])).
% 0.17/0.35 tff(27,plain,
% 0.17/0.35 (((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~((~p(tptp_fun_Y_0(elem!1))) | q(tptp_fun_Y_0(elem!1)) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) <=> ((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~(q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.17/0.35 inference(monotonicity,[status(thm)],[26])).
% 0.17/0.35 tff(28,plain,
% 0.17/0.35 (((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~((~p(tptp_fun_Y_0(elem!1))) | q(tptp_fun_Y_0(elem!1)) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))) <=> ((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~(q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.17/0.35 inference(transitivity,[status(thm)],[27, 25])).
% 0.17/0.35 tff(29,plain,
% 0.17/0.35 ((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~((~p(tptp_fun_Y_0(elem!1))) | q(tptp_fun_Y_0(elem!1)) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))),
% 0.17/0.35 inference(quant_inst,[status(thm)],[])).
% 0.17/0.35 tff(30,plain,
% 0.17/0.35 ((~![X: $i] : (~((~p(X)) | q(X) | p(tptp_fun_Y_0(X))))) | (~(q(tptp_fun_Y_0(elem!1)) | (~p(tptp_fun_Y_0(elem!1))) | p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1)))))),
% 0.17/0.35 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.17/0.35 tff(31,plain,
% 0.17/0.35 ($false),
% 0.17/0.35 inference(unit_resolution,[status(thm)],[30, 18, 24])).
% 0.17/0.35 % SZS output end Proof
% 0.17/0.35 % E exiting
%------------------------------------------------------------------------------