%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN360+1 : TPTP v9.0.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:38:53 AM UTC 2025
% Result : Theorem 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN360+1 : TPTP v9.0.0. Released v2.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:36:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Theorem
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(big_p_type, type, (
% 0.18/0.37 big_p: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.18/0.37 tptp_fun_Y_0: $i > $i)).
% 0.18/0.37 tff(tptp_fun_X_1_type, type, (
% 0.18/0.37 tptp_fun_X_1: $i)).
% 0.18/0.37 tff(big_q_type, type, (
% 0.18/0.37 big_q: ( $i * $i ) > $o)).
% 0.18/0.37 tff(tptp_fun_Y_2_type, type, (
% 0.18/0.37 tptp_fun_Y_2: $i)).
% 0.18/0.37 tff(1,plain,
% 0.18/0.37 (![Z: $i] : ?[Y: $i] : big_p(Z, Y) <=> ![Z: $i] : ?[Y: $i] : big_p(Z, Y)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 ((~((![X: $i] : (?[Y: $i] : big_p(X, Y) => ![Y: $i] : big_q(X, Y)) & ![Z: $i] : ?[Y: $i] : big_p(Z, Y)) => ![Y: $i, X: $i] : big_q(X, Y))) <=> (~((~(![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) & ![Z: $i] : ?[Y: $i] : big_p(Z, Y))) | ![Y: $i, X: $i] : big_q(X, Y)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(3,axiom,(~((![X: $i] : (?[Y: $i] : big_p(X, Y) => ![Y: $i] : big_q(X, Y)) & ![Z: $i] : ?[Y: $i] : big_p(Z, Y)) => ![Y: $i, X: $i] : big_q(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2111')).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (~((~(![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) & ![Z: $i] : ?[Y: $i] : big_p(Z, Y))) | ![Y: $i, X: $i] : big_q(X, Y))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) & ![Z: $i] : ?[Y: $i] : big_p(Z, Y)),
% 0.18/0.37 inference(or_elim,[status(thm)],[4])).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (![Z: $i] : ?[Y: $i] : big_p(Z, Y)),
% 0.18/0.37 inference(and_elim,[status(thm)],[5])).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![Z: $i] : ?[Y: $i] : big_p(Z, Y)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.37 tff(8,plain,(
% 0.18/0.37 ![Z: $i] : big_p(Z, tptp_fun_Y_0(Z))),
% 0.18/0.37 inference(skolemize,[status(sab)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~![Z: $i] : big_p(Z, tptp_fun_Y_0(Z))) | big_p(X!1, tptp_fun_Y_0(X!1))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 (big_p(X!1, tptp_fun_Y_0(X!1))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 ((~![Y: $i, X: $i] : big_q(X, Y)) <=> (~![Y: $i, X: $i] : big_q(X, Y))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(12,plain,
% 0.18/0.37 (~![Y: $i, X: $i] : big_q(X, Y)),
% 0.18/0.37 inference(or_elim,[status(thm)],[4])).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (~![Y: $i, X: $i] : big_q(X, Y)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (~![Y: $i, X: $i] : big_q(X, Y)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[13, 11])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (~![Y: $i, X: $i] : big_q(X, Y)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.18/0.37 tff(16,plain,(
% 0.18/0.37 ~big_q(X!1, Y!2)),
% 0.18/0.37 inference(skolemize,[status(sab)],[15])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (^[X: $i, Y_3: $i, Y: $i] : refl(((~big_p(X, Y)) | big_q(X, Y_3)) <=> ((~big_p(X, Y)) | big_q(X, Y_3)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3)) <=> ![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![X: $i] : ![Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3)) <=> ![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(pull_quant,[status(thm)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (^[X: $i] : pull_quant((![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![X: $i] : ![Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(transitivity,[status(thm)],[21, 19])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(transitivity,[status(thm)],[22, 18])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (^[X: $i] : rewrite((![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y)) <=> ![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y))),
% 0.18/0.37 inference(and_elim,[status(thm)],[5])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (![X: $i] : ((~?[Y: $i] : big_p(X, Y)) | ![Y: $i] : big_q(X, Y))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.18/0.37 tff(30,plain,(
% 0.18/0.37 ![X: $i] : (![Y: $i] : (~big_p(X, Y)) | ![Y: $i] : big_q(X, Y))),
% 0.18/0.37 inference(skolemize,[status(sab)],[29])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (((~![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))) | ((~big_p(X!1, tptp_fun_Y_0(X!1))) | big_q(X!1, Y!2))) <=> ((~![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))) | (~big_p(X!1, tptp_fun_Y_0(X!1))) | big_q(X!1, Y!2))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 ((~![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))) | ((~big_p(X!1, tptp_fun_Y_0(X!1))) | big_q(X!1, Y!2))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 ((~![X: $i, Y_3: $i, Y: $i] : ((~big_p(X, Y)) | big_q(X, Y_3))) | (~big_p(X!1, tptp_fun_Y_0(X!1))) | big_q(X!1, Y!2)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[34, 31, 16, 10])).
% 0.18/0.37 % SZS output end Proof
% 0.18/0.37 % E exiting
%------------------------------------------------------------------------------