%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN049+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:38:02 AM UTC 2025
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN049+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.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 12:26:35 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% 0.11/0.36 tff(big_p_type, type, (
% 0.11/0.36 big_p: $i > $o)).
% 0.11/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.36 tptp_fun_Y_1: $i > $i)).
% 0.11/0.36 tff(tptp_fun_Z_0_type, type, (
% 0.11/0.36 tptp_fun_Z_0: $i > $i)).
% 0.11/0.36 tff(elem_2_type, type, (
% 0.11/0.36 elem_2: $i)).
% 0.11/0.36 tff(big_q_type, type, (
% 0.11/0.36 big_q: $i > $o)).
% 0.11/0.36 tff(1,assumption,(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))), introduced(assumption)).
% 0.11/0.36 tff(2,plain,
% 0.11/0.36 (^[X: $i] : refl((~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))) <=> (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(3,plain,
% 0.11/0.36 (![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))) <=> ![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.11/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.36 tff(4,plain,
% 0.11/0.36 ((~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(5,plain,
% 0.11/0.36 ((~?[X: $i] : ![Y: $i, Z: $i] : ((big_p(Y) => big_q(Z)) => (big_p(X) => big_q(X)))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y))))))),
% 0.11/0.36 inference(rewrite,[status(thm)],[])).
% 0.11/0.36 tff(6,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : ((big_p(Y) => big_q(Z)) => (big_p(X) => big_q(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel19')).
% 0.11/0.36 tff(7,plain,
% 0.11/0.36 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.36 tff(8,plain,
% 0.11/0.36 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[7, 4])).
% 0.11/0.36 tff(9,plain,
% 0.11/0.36 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.36 tff(10,plain,
% 0.11/0.36 (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.11/0.36 tff(11,plain,
% 0.11/0.36 (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))), (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))))),
% 0.11/0.36 inference(bind,[status(th)],[])).
% 0.11/0.36 tff(12,plain,(
% 0.11/0.36 ![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.11/0.36 inference(nnf-neg,[status(sab)],[10, 11])).
% 0.11/0.36 tff(13,plain,
% 0.11/0.36 (![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.11/0.36 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.11/0.36 tff(14,plain,
% 0.11/0.36 ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(15,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[14, 13, 1])).
% 0.11/0.36 tff(16,plain,(~(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.36 tff(17,plain,
% 0.11/0.36 ((big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))) | big_p(tptp_fun_Y_1(elem!2))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(18,plain,
% 0.11/0.36 (big_p(tptp_fun_Y_1(elem!2))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.11/0.36 tff(19,plain,
% 0.11/0.36 ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(20,plain,
% 0.11/0.36 (~(big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.11/0.36 tff(21,plain,
% 0.11/0.36 ((big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))))) | (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(22,plain,
% 0.11/0.36 (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.11/0.36 tff(23,plain,
% 0.11/0.36 ((~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))) | big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(24,plain,
% 0.11/0.36 (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.11/0.36 tff(25,plain,
% 0.11/0.36 (big_q(tptp_fun_Z_0(elem!2))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.11/0.36 tff(26,plain,
% 0.11/0.36 ((big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_q(tptp_fun_Z_0(elem!2)))),
% 0.11/0.36 inference(tautology,[status(thm)],[])).
% 0.11/0.36 tff(27,plain,
% 0.11/0.36 (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.11/0.36 tff(28,plain,
% 0.11/0.36 ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.11/0.36 inference(quant_inst,[status(thm)],[])).
% 0.11/0.36 tff(29,plain,
% 0.11/0.36 ($false),
% 0.11/0.36 inference(unit_resolution,[status(thm)],[28, 13, 27])).
% 0.11/0.36 % SZS output end Proof
% 0.11/0.36 % E exiting
%------------------------------------------------------------------------------