%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN382+1 : TPTP v9.0.0. Released v2.0.0.
% 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 05:38:56 AM UTC 2025
% Result : Theorem 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN382+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 12:33:07 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(big_p_type, type, (
% 0.11/0.37 big_p: ( $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Y_1_type, type, (
% 0.11/0.37 tptp_fun_Y_1: $i)).
% 0.11/0.37 tff(tptp_fun_X_0_type, type, (
% 0.11/0.37 tptp_fun_X_0: $i > $i)).
% 0.11/0.37 tff(big_q_type, type, (
% 0.11/0.37 big_q: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,assumption,(big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[X: $i] : refl((~(big_p(X, Y!1) | big_q(X, Y!1))) <=> (~(big_p(X, Y!1) | big_q(X, Y!1))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1))) <=> ![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 ((~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))) <=> (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 ((~(![Z: $i] : ?[X: $i] : (![Y: $i] : big_p(X, Y) | big_q(X, Z)) => ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))) <=> (~((~![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))) | ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,axiom,(~(![Z: $i] : ?[X: $i] : (![Y: $i] : big_p(X, Y) | big_q(X, Z)) => ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2134')).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (~((~![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))) | ![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.11/0.37 inference(or_elim,[status(thm)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 4])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 (~![Y: $i] : ?[X: $i] : (big_p(X, Y) | big_q(X, Y))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.11/0.37 tff(12,plain,(
% 0.11/0.37 $oeq((~?[X: $i] : (big_p(X, Y!1) | big_q(X, Y!1))), ![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1))))),
% 0.11/0.37 inference(transitivity,[status(sab)],[11])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 ((~![X: $i] : (~(big_p(X, Y!1) | big_q(X, Y!1)))) | (~(big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[14, 13, 1])).
% 0.11/0.37 tff(16,plain,(~(big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 ((big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)) | (~big_p(tptp_fun_X_0(Y!1), Y!1))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 (~big_p(tptp_fun_X_0(Y!1), Y!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((big_p(tptp_fun_X_0(Y!1), Y!1) | big_q(tptp_fun_X_0(Y!1), Y!1)) | (~big_q(tptp_fun_X_0(Y!1), Y!1))),
% 0.11/0.37 inference(tautology,[status(thm)],[])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (~big_q(tptp_fun_X_0(Y!1), Y!1)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[19, 16])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 (![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y)) <=> ![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))),
% 0.11/0.37 inference(or_elim,[status(thm)],[7])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (![Z: $i] : ?[X: $i] : (big_q(X, Z) | ![Y: $i] : big_p(X, Y))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.37 tff(24,plain,(
% 0.11/0.37 ![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))),
% 0.11/0.37 inference(skolemize,[status(sab)],[23])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | (big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y))) <=> ((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 ((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | (big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 ((~![Z: $i] : (big_q(tptp_fun_X_0(Z), Z) | ![Y: $i] : big_p(tptp_fun_X_0(Z), Y))) | big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (big_q(tptp_fun_X_0(Y!1), Y!1) | ![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[27, 24])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[28, 20])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~![Y: $i] : big_p(tptp_fun_X_0(Y!1), Y)) | big_p(tptp_fun_X_0(Y!1), Y!1)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[30, 29, 18])).
% 0.11/0.37 % SZS output end Proof
% 0.11/0.37 % E exiting
%------------------------------------------------------------------------------