%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:05 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n026.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 5 06:33:57 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(is_a_theorem_type, type, (
% 0.13/0.40 is_a_theorem: $i > $o)).
% 0.13/0.40 tff(implies_type, type, (
% 0.13/0.40 implies: ( $i * $i ) > $i)).
% 0.13/0.40 tff(or_type, type, (
% 0.13/0.40 or: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_Q_45_type, type, (
% 0.13/0.40 tptp_fun_Q_45: $i)).
% 0.13/0.40 tff(tptp_fun_P_46_type, type, (
% 0.13/0.40 tptp_fun_P_46: $i)).
% 0.13/0.40 tff(r2_type, type, (
% 0.13/0.40 r2: $o)).
% 0.13/0.40 tff(or_2_type, type, (
% 0.13/0.40 or_2: $o)).
% 0.13/0.40 tff(tptp_fun_Y_21_type, type, (
% 0.13/0.40 tptp_fun_Y_21: $i)).
% 0.13/0.40 tff(tptp_fun_X_22_type, type, (
% 0.13/0.40 tptp_fun_X_22: $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 ((~r2) <=> (~r2)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(2,axiom,(~r2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','principia_r2')).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (~r2),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (((~r2) | ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> ((~r2) | ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 ((((~r2) | ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) & (r2 | (~is_a_theorem(implies(Q!45, or(P!46, Q!45)))))) <=> (((~r2) | ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) & (r2 | (~is_a_theorem(implies(Q!45, or(P!46, Q!45))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[4])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 ((r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) <=> (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(7,axiom,(r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','r2')).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 6])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (r2 <=> ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.13/0.40 tff(12,plain,(
% 0.13/0.40 ((~r2) | ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) & (r2 | (~is_a_theorem(implies(Q!45, or(P!46, Q!45)))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[11])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (((~r2) | ![P: $i, Q: $i] : is_a_theorem(implies(Q, or(P, Q)))) & (r2 | (~is_a_theorem(implies(Q!45, or(P!46, Q!45)))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (r2 | (~is_a_theorem(implies(Q!45, or(P!46, Q!45))))),
% 0.13/0.40 inference(and_elim,[status(thm)],[13])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (~is_a_theorem(implies(Q!45, or(P!46, Q!45)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[14, 3])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (or_2 <=> or_2),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(17,axiom,(or_2), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax','hilbert_or_2')).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (or_2),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> ((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 ((((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) & (or_2 | (~is_a_theorem(implies(Y!21, or(X!22, Y!21)))))) <=> (((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) & (or_2 | (~is_a_theorem(implies(Y!21, or(X!22, Y!21))))))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) <=> (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(23,axiom,(or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax','or_2')).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[24, 22])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (or_2 <=> ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.13/0.41 tff(28,plain,(
% 0.13/0.41 ((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) & (or_2 | (~is_a_theorem(implies(Y!21, or(X!22, Y!21)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[27])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) & (or_2 | (~is_a_theorem(implies(Y!21, or(X!22, Y!21)))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 ((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(and_elim,[status(thm)],[29])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 ((~or_2) | ![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[30, 19])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[31, 18])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 ((~![X: $i, Y: $i] : is_a_theorem(implies(Y, or(X, Y)))) | is_a_theorem(implies(Q!45, or(P!46, Q!45)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[33, 32, 15])).
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------