%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN383+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:56 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN383+1 : TPTP v9.0.0. Released v2.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:35:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(big_q_type, type, (
% 0.19/0.36 big_q: $i > $o)).
% 0.19/0.36 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.36 tptp_fun_Y_0: $i > $i)).
% 0.19/0.36 tff(elem_1_type, type, (
% 0.19/0.36 elem_1: $i)).
% 0.19/0.36 tff(big_p_type, type, (
% 0.19/0.36 big_p: $i > $o)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (^[X: $i] : refl((~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X))))) <=> (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X))))) <=> ![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X)))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (^[X: $i] : rewrite((~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~(big_p(X) & big_q(tptp_fun_Y_0(X)))))) <=> (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~(big_p(X) & big_q(tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X)))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.36 tff(5,plain,
% 0.19/0.36 ((~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y))))) <=> (~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(6,plain,
% 0.19/0.36 ((~?[X: $i] : ![Y: $i] : ((big_p(X) & big_q(Y)) => (big_q(X) | big_p(Y)))) <=> (~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y)))))),
% 0.19/0.36 inference(rewrite,[status(thm)],[])).
% 0.19/0.36 tff(7,axiom,(~?[X: $i] : ![Y: $i] : ((big_p(X) & big_q(Y)) => (big_q(X) | big_p(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2135')).
% 0.19/0.36 tff(8,plain,
% 0.19/0.36 (~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.36 tff(9,plain,
% 0.19/0.36 (~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.19/0.36 tff(10,plain,
% 0.19/0.36 (~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.36 tff(11,plain,
% 0.19/0.36 (~?[X: $i] : ![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.19/0.36 tff(12,plain,
% 0.19/0.36 (^[X: $i] : sk($oeq((~![Y: $i] : (big_q(X) | big_p(Y) | (~(big_p(X) & big_q(Y))))), (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~(big_p(X) & big_q(tptp_fun_Y_0(X))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(13,plain,(
% 0.19/0.36 ![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~(big_p(X) & big_q(tptp_fun_Y_0(X))))))),
% 0.19/0.36 inference(nnf-neg,[status(sab)],[11, 12])).
% 0.19/0.36 tff(14,plain,
% 0.19/0.36 (![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.19/0.36 tff(15,plain,
% 0.19/0.36 (![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X)))))),
% 0.19/0.36 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.19/0.36 tff(16,plain,
% 0.19/0.36 ((~![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X)))))) | (~(big_q(elem!1) | big_p(tptp_fun_Y_0(elem!1)) | (~big_p(elem!1)) | (~big_q(tptp_fun_Y_0(elem!1)))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(17,plain,
% 0.19/0.36 (~(big_q(elem!1) | big_p(tptp_fun_Y_0(elem!1)) | (~big_p(elem!1)) | (~big_q(tptp_fun_Y_0(elem!1))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.36 tff(18,plain,
% 0.19/0.36 ((big_q(elem!1) | big_p(tptp_fun_Y_0(elem!1)) | (~big_p(elem!1)) | (~big_q(tptp_fun_Y_0(elem!1)))) | big_q(tptp_fun_Y_0(elem!1))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(19,plain,
% 0.19/0.36 (big_q(tptp_fun_Y_0(elem!1))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.19/0.36 tff(20,plain,
% 0.19/0.36 ((big_q(tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_p(tptp_fun_Y_0(elem!1))) | (~big_q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))) | (~big_q(tptp_fun_Y_0(elem!1)))),
% 0.19/0.36 inference(tautology,[status(thm)],[])).
% 0.19/0.36 tff(21,plain,
% 0.19/0.36 (big_q(tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_p(tptp_fun_Y_0(elem!1))) | (~big_q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.19/0.36 tff(22,plain,
% 0.19/0.36 ((~![X: $i] : (~(big_q(X) | big_p(tptp_fun_Y_0(X)) | (~big_p(X)) | (~big_q(tptp_fun_Y_0(X)))))) | (~(big_q(tptp_fun_Y_0(elem!1)) | big_p(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))) | (~big_p(tptp_fun_Y_0(elem!1))) | (~big_q(tptp_fun_Y_0(tptp_fun_Y_0(elem!1))))))),
% 0.19/0.36 inference(quant_inst,[status(thm)],[])).
% 0.19/0.36 tff(23,plain,
% 0.19/0.36 ($false),
% 0.19/0.36 inference(unit_resolution,[status(thm)],[22, 15, 21])).
% 0.19/0.36 % SZS output end Proof
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------