%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN355+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 05:38:52 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN355+1 : TPTP v9.0.0. Released v2.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:35:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(big_r_type, type, (
% 0.12/0.37 big_r: $i > $o)).
% 0.12/0.37 tff(tptp_fun_X_0_type, type, (
% 0.12/0.37 tptp_fun_X_0: $i)).
% 0.12/0.37 tff(big_p_type, type, (
% 0.12/0.37 big_p: $i > $o)).
% 0.12/0.37 tff(big_q_type, type, (
% 0.12/0.37 big_q: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 ((~![X: $i] : (big_p(X) | big_q(X))) <=> (~![X: $i] : (big_p(X) | big_q(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 ((~((![X: $i] : (big_r(X) => big_p(X)) & ![X: $i] : ((~big_q(X)) => big_r(X))) => ![X: $i] : (big_p(X) | big_q(X)))) <=> (~((~(![X: $i] : (big_p(X) | (~big_r(X))) & ![X: $i] : (big_q(X) | big_r(X)))) | ![X: $i] : (big_p(X) | big_q(X))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,axiom,(~((![X: $i] : (big_r(X) => big_p(X)) & ![X: $i] : ((~big_q(X)) => big_r(X))) => ![X: $i] : (big_p(X) | big_q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2106')).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (~((~(![X: $i] : (big_p(X) | (~big_r(X))) & ![X: $i] : (big_q(X) | big_r(X)))) | ![X: $i] : (big_p(X) | big_q(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (~![X: $i] : (big_p(X) | big_q(X))),
% 0.12/0.37 inference(or_elim,[status(thm)],[4])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (~![X: $i] : (big_p(X) | big_q(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (~![X: $i] : (big_p(X) | big_q(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (~![X: $i] : (big_p(X) | big_q(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.37 tff(9,plain,(
% 0.12/0.37 ~(big_p(X!0) | big_q(X!0))),
% 0.12/0.37 inference(skolemize,[status(sab)],[8])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (~big_p(X!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[9])).
% 0.12/0.37 tff(11,plain,
% 0.12/0.37 (^[X: $i] : refl((big_p(X) | (~big_r(X))) <=> (big_p(X) | (~big_r(X))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![X: $i] : (big_p(X) | (~big_r(X))) <=> ![X: $i] : (big_p(X) | (~big_r(X)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![X: $i] : (big_p(X) | (~big_r(X))) <=> ![X: $i] : (big_p(X) | (~big_r(X)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(14,plain,
% 0.12/0.37 (![X: $i] : (big_p(X) | (~big_r(X))) & ![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(or_elim,[status(thm)],[4])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![X: $i] : (big_p(X) | (~big_r(X)))),
% 0.12/0.37 inference(and_elim,[status(thm)],[14])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![X: $i] : (big_p(X) | (~big_r(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.12/0.37 tff(17,plain,(
% 0.12/0.37 ![X: $i] : (big_p(X) | (~big_r(X)))),
% 0.12/0.37 inference(skolemize,[status(sab)],[16])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (![X: $i] : (big_p(X) | (~big_r(X)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~![X: $i] : (big_p(X) | (~big_r(X)))) | (big_p(X!0) | (~big_r(X!0)))) <=> ((~![X: $i] : (big_p(X) | (~big_r(X)))) | big_p(X!0) | (~big_r(X!0)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 ((~![X: $i] : (big_p(X) | (~big_r(X)))) | (big_p(X!0) | (~big_r(X!0)))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![X: $i] : (big_p(X) | (~big_r(X)))) | big_p(X!0) | (~big_r(X!0))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 (~big_r(X!0)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[21, 18, 10])).
% 0.12/0.37 tff(23,plain,
% 0.12/0.37 (~big_q(X!0)),
% 0.12/0.37 inference(or_elim,[status(thm)],[9])).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (^[X: $i] : refl((big_q(X) | big_r(X)) <=> (big_q(X) | big_r(X)))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (![X: $i] : (big_q(X) | big_r(X)) <=> ![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (![X: $i] : (big_q(X) | big_r(X)) <=> ![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(and_elim,[status(thm)],[14])).
% 0.12/0.37 tff(28,plain,
% 0.12/0.37 (![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.12/0.37 tff(29,plain,(
% 0.12/0.37 ![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(skolemize,[status(sab)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 (![X: $i] : (big_q(X) | big_r(X))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 (((~![X: $i] : (big_q(X) | big_r(X))) | (big_q(X!0) | big_r(X!0))) <=> ((~![X: $i] : (big_q(X) | big_r(X))) | big_q(X!0) | big_r(X!0))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 ((~![X: $i] : (big_q(X) | big_r(X))) | (big_q(X!0) | big_r(X!0))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 ((~![X: $i] : (big_q(X) | big_r(X))) | big_q(X!0) | big_r(X!0)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 30, 23, 22])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------