%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN372+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 05:38:55 AM UTC 2025
% Result : Theorem 0.12s 0.36s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN372+1 : TPTP v9.0.0. Released v2.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 12:32:07 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 tff(big_p_type, type, (
% 0.12/0.36 big_p: $i > $o)).
% 0.12/0.36 tff(tptp_fun_X_0_type, type, (
% 0.12/0.36 tptp_fun_X_0: $i)).
% 0.12/0.36 tff(big_q_type, type, (
% 0.12/0.36 big_q: $i > $o)).
% 0.12/0.36 tff(tptp_fun_Y_1_type, type, (
% 0.12/0.36 tptp_fun_Y_1: $i)).
% 0.12/0.36 tff(1,assumption,(big_q(Y!1) | (~big_p(Y!1))), introduced(assumption)).
% 0.12/0.36 tff(2,plain,
% 0.12/0.36 (^[Y: $i] : refl((~(big_q(Y) | (~big_p(Y)))) <=> (~(big_q(Y) | (~big_p(Y)))))),
% 0.12/0.36 inference(bind,[status(th)],[])).
% 0.12/0.36 tff(3,plain,
% 0.12/0.36 (![Y: $i] : (~(big_q(Y) | (~big_p(Y)))) <=> ![Y: $i] : (~(big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.36 tff(4,plain,
% 0.12/0.36 (((big_q(X!0) | (~big_p(Y!1))) & ![Y: $i] : (~(big_q(Y) | (~big_p(Y))))) <=> ((big_q(X!0) | (~big_p(Y!1))) & ![Y: $i] : (~(big_q(Y) | (~big_p(Y)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(5,plain,
% 0.12/0.36 ((~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y))))) <=> (~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(6,plain,
% 0.12/0.36 ((~![X: $i] : (?[Y: $i] : (big_p(Y) => big_q(X)) => ?[Y: $i] : (big_p(Y) => big_q(Y)))) <=> (~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y)))))),
% 0.12/0.36 inference(rewrite,[status(thm)],[])).
% 0.12/0.36 tff(7,axiom,(~![X: $i] : (?[Y: $i] : (big_p(Y) => big_q(X)) => ?[Y: $i] : (big_p(Y) => big_q(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','x2123')).
% 0.12/0.36 tff(8,plain,
% 0.12/0.36 (~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.36 tff(9,plain,
% 0.12/0.36 (~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.36 tff(10,plain,
% 0.12/0.36 (~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.36 tff(11,plain,
% 0.12/0.36 (~![X: $i] : ((~?[Y: $i] : (big_q(X) | (~big_p(Y)))) | ?[Y: $i] : (big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.36 tff(12,plain,
% 0.12/0.36 ((big_q(X!0) | (~big_p(Y!1))) & ![Y: $i] : (~(big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.36 tff(13,plain,
% 0.12/0.36 (![Y: $i] : (~(big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(and_elim,[status(thm)],[12])).
% 0.12/0.36 tff(14,plain,
% 0.12/0.36 (![Y: $i] : (~(big_q(Y) | (~big_p(Y))))),
% 0.12/0.36 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.12/0.36 tff(15,plain,
% 0.12/0.36 ((~![Y: $i] : (~(big_q(Y) | (~big_p(Y))))) | (~(big_q(Y!1) | (~big_p(Y!1))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(16,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.12/0.36 tff(17,plain,(~(big_q(Y!1) | (~big_p(Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.36 tff(18,plain,
% 0.12/0.36 ((big_q(Y!1) | (~big_p(Y!1))) | big_p(Y!1)),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(19,plain,
% 0.12/0.36 (big_p(Y!1)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.12/0.36 tff(20,plain,
% 0.12/0.36 (big_q(X!0) | (~big_p(Y!1))),
% 0.12/0.36 inference(and_elim,[status(thm)],[12])).
% 0.12/0.36 tff(21,plain,
% 0.12/0.36 (big_q(X!0)),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.12/0.36 tff(22,plain,
% 0.12/0.36 ((big_q(X!0) | (~big_p(X!0))) | (~big_q(X!0))),
% 0.12/0.36 inference(tautology,[status(thm)],[])).
% 0.12/0.36 tff(23,plain,
% 0.12/0.36 (big_q(X!0) | (~big_p(X!0))),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.12/0.36 tff(24,plain,
% 0.12/0.36 ((~![Y: $i] : (~(big_q(Y) | (~big_p(Y))))) | (~(big_q(X!0) | (~big_p(X!0))))),
% 0.12/0.36 inference(quant_inst,[status(thm)],[])).
% 0.12/0.36 tff(25,plain,
% 0.12/0.36 ($false),
% 0.12/0.36 inference(unit_resolution,[status(thm)],[24, 14, 23])).
% 0.12/0.36 % SZS output end Proof
% 0.12/0.36 % E exiting
%------------------------------------------------------------------------------