TSTP Solution File: LCL239-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Sun Sep 18 04:55:35 EDT 2022
% Result : Unsatisfiable 4.13s 2.88s
% Output : Proof 4.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL239-3 : TPTP v8.1.0. Released v2.3.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Sep 1 19:18:58 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 4.13/2.88 % SZS status Unsatisfiable
% 4.13/2.88 % SZS output start Proof
% 4.13/2.88 tff(theorem_type, type, (
% 4.13/2.88 theorem: $i > $o)).
% 4.13/2.88 tff(implies_type, type, (
% 4.13/2.88 implies: ( $i * $i ) > $i)).
% 4.13/2.88 tff(or_type, type, (
% 4.13/2.88 or: ( $i * $i ) > $i)).
% 4.13/2.88 tff(not_type, type, (
% 4.13/2.88 not: $i > $i)).
% 4.13/2.88 tff(p_type, type, (
% 4.13/2.88 p: $i)).
% 4.13/2.88 tff(and_type, type, (
% 4.13/2.88 and: ( $i * $i ) > $i)).
% 4.13/2.88 tff(axiom_type, type, (
% 4.13/2.88 axiom: $i > $o)).
% 4.13/2.88 tff(1,plain,
% 4.13/2.88 (^[Q: $i, P: $i] : refl((and(P, Q) = not(or(not(P), not(Q)))) <=> (and(P, Q) = not(or(not(P), not(Q)))))),
% 4.13/2.88 inference(bind,[status(th)],[])).
% 4.13/2.88 tff(2,plain,
% 4.13/2.88 (![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q)))) <=> ![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))),
% 4.13/2.88 inference(quant_intro,[status(thm)],[1])).
% 4.13/2.88 tff(3,plain,
% 4.13/2.88 (![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q)))) <=> ![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))),
% 4.13/2.88 inference(rewrite,[status(thm)],[])).
% 4.13/2.88 tff(4,axiom,(![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-1.ax','and_defn')).
% 4.13/2.88 tff(5,plain,
% 4.13/2.88 (![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))),
% 4.13/2.88 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.13/2.88 tff(6,plain,(
% 4.13/2.88 ![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))),
% 4.13/2.88 inference(skolemize,[status(sab)],[5])).
% 4.13/2.88 tff(7,plain,
% 4.13/2.88 (![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))),
% 4.13/2.88 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.13/2.88 tff(8,plain,
% 4.13/2.88 ((~![Q: $i, P: $i] : (and(P, Q) = not(or(not(P), not(Q))))) | (and(p, not(p)) = not(or(not(p), not(not(p)))))),
% 4.13/2.88 inference(quant_inst,[status(thm)],[])).
% 4.13/2.88 tff(9,plain,
% 4.13/2.88 (and(p, not(p)) = not(or(not(p), not(not(p))))),
% 4.13/2.88 inference(unit_resolution,[status(thm)],[8, 7])).
% 4.13/2.88 tff(10,plain,
% 4.13/2.88 (not(or(not(p), not(not(p)))) = and(p, not(p))),
% 4.13/2.88 inference(symmetry,[status(thm)],[9])).
% 4.13/2.88 tff(11,plain,
% 4.13/2.88 (not(not(or(not(p), not(not(p))))) = not(and(p, not(p)))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[10])).
% 4.13/2.88 tff(12,plain,
% 4.13/2.88 (not(and(p, not(p))) = not(not(or(not(p), not(not(p)))))),
% 4.13/2.88 inference(symmetry,[status(thm)],[11])).
% 4.13/2.88 tff(13,plain,
% 4.13/2.88 (or(not(and(p, not(p))), not(or(not(p), not(not(p))))) = or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[12])).
% 4.13/2.88 tff(14,plain,
% 4.13/2.88 (or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))) = or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[13])).
% 4.13/2.88 tff(15,plain,
% 4.13/2.88 (or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) = or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))),
% 4.13/2.88 inference(symmetry,[status(thm)],[14])).
% 4.13/2.88 tff(16,plain,
% 4.13/2.88 (^[Y: $i, X: $i] : refl((implies(X, Y) = or(not(X), Y)) <=> (implies(X, Y) = or(not(X), Y)))),
% 4.13/2.88 inference(bind,[status(th)],[])).
% 4.13/2.88 tff(17,plain,
% 4.13/2.88 (![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))),
% 4.13/2.88 inference(quant_intro,[status(thm)],[16])).
% 4.13/2.88 tff(18,plain,
% 4.13/2.88 (![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y)) <=> ![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))),
% 4.13/2.88 inference(rewrite,[status(thm)],[])).
% 4.13/2.88 tff(19,axiom,(![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax','implies_definition')).
% 4.13/2.88 tff(20,plain,
% 4.13/2.88 (![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))),
% 4.13/2.88 inference(modus_ponens,[status(thm)],[19, 18])).
% 4.13/2.88 tff(21,plain,(
% 4.13/2.88 ![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))),
% 4.13/2.88 inference(skolemize,[status(sab)],[20])).
% 4.13/2.88 tff(22,plain,
% 4.13/2.88 (![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))),
% 4.13/2.88 inference(modus_ponens,[status(thm)],[21, 17])).
% 4.13/2.88 tff(23,plain,
% 4.13/2.88 ((~![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) = or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))),
% 4.13/2.88 inference(quant_inst,[status(thm)],[])).
% 4.13/2.88 tff(24,plain,
% 4.13/2.88 (implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) = or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))),
% 4.13/2.88 inference(unit_resolution,[status(thm)],[23, 22])).
% 4.13/2.88 tff(25,plain,
% 4.13/2.88 (implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) = or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))),
% 4.13/2.88 inference(transitivity,[status(thm)],[24, 15])).
% 4.13/2.88 tff(26,plain,
% 4.13/2.88 (theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))) <=> theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[25])).
% 4.13/2.88 tff(27,plain,
% 4.13/2.88 (theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) <=> theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))),
% 4.13/2.88 inference(symmetry,[status(thm)],[26])).
% 4.13/2.88 tff(28,plain,
% 4.13/2.88 (or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))) = or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[12])).
% 4.13/2.88 tff(29,plain,
% 4.13/2.88 (implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) = implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[28])).
% 4.13/2.88 tff(30,plain,
% 4.13/2.88 (theorem(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))) <=> theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))),
% 4.13/2.88 inference(monotonicity,[status(thm)],[29])).
% 4.13/2.88 tff(31,plain,
% 4.13/2.88 (^[B: $i, A: $i, C: $i] : refl(axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) <=> axiom(implies(or(A, or(B, C)), or(B, or(A, C)))))),
% 4.13/2.88 inference(bind,[status(th)],[])).
% 4.13/2.88 tff(32,plain,
% 4.13/2.88 (![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) <=> ![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))),
% 4.13/2.88 inference(quant_intro,[status(thm)],[31])).
% 4.13/2.88 tff(33,plain,
% 4.13/2.88 (![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) <=> ![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))),
% 4.13/2.88 inference(rewrite,[status(thm)],[])).
% 4.13/2.88 tff(34,axiom,(![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax','axiom_1_5')).
% 4.13/2.88 tff(35,plain,
% 4.13/2.88 (![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))),
% 4.13/2.88 inference(modus_ponens,[status(thm)],[34, 33])).
% 4.13/2.88 tff(36,plain,(
% 4.13/2.89 ![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))),
% 4.13/2.89 inference(skolemize,[status(sab)],[35])).
% 4.13/2.89 tff(37,plain,
% 4.13/2.89 (![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[36, 32])).
% 4.13/2.89 tff(38,plain,
% 4.13/2.89 ((~![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))) | axiom(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))),
% 4.13/2.89 inference(quant_inst,[status(thm)],[])).
% 4.13/2.89 tff(39,plain,
% 4.13/2.89 (axiom(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))),
% 4.13/2.89 inference(unit_resolution,[status(thm)],[38, 37])).
% 4.13/2.89 tff(40,plain,
% 4.13/2.89 (^[X: $i] : refl((theorem(X) | (~axiom(X))) <=> (theorem(X) | (~axiom(X))))),
% 4.13/2.89 inference(bind,[status(th)],[])).
% 4.13/2.89 tff(41,plain,
% 4.13/2.89 (![X: $i] : (theorem(X) | (~axiom(X))) <=> ![X: $i] : (theorem(X) | (~axiom(X)))),
% 4.13/2.89 inference(quant_intro,[status(thm)],[40])).
% 4.13/2.89 tff(42,plain,
% 4.13/2.89 (![X: $i] : (theorem(X) | (~axiom(X))) <=> ![X: $i] : (theorem(X) | (~axiom(X)))),
% 4.13/2.89 inference(rewrite,[status(thm)],[])).
% 4.13/2.89 tff(43,axiom,(![X: $i] : (theorem(X) | (~axiom(X)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax','rule_1')).
% 4.13/2.89 tff(44,plain,
% 4.13/2.89 (![X: $i] : (theorem(X) | (~axiom(X)))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.13/2.89 tff(45,plain,(
% 4.13/2.89 ![X: $i] : (theorem(X) | (~axiom(X)))),
% 4.13/2.89 inference(skolemize,[status(sab)],[44])).
% 4.13/2.89 tff(46,plain,
% 4.13/2.89 (![X: $i] : (theorem(X) | (~axiom(X)))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[45, 41])).
% 4.13/2.89 tff(47,plain,
% 4.13/2.89 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))) | (~axiom(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))) | (~axiom(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))))),
% 4.13/2.89 inference(rewrite,[status(thm)],[])).
% 4.13/2.89 tff(48,plain,
% 4.13/2.89 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))) | (~axiom(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))))),
% 4.13/2.89 inference(quant_inst,[status(thm)],[])).
% 4.13/2.89 tff(49,plain,
% 4.13/2.89 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))) | (~axiom(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[48, 47])).
% 4.13/2.89 tff(50,plain,
% 4.13/2.89 (theorem(implies(or(not(and(p, not(p))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))),
% 4.13/2.89 inference(unit_resolution,[status(thm)],[49, 46, 39])).
% 4.13/2.89 tff(51,plain,
% 4.13/2.89 (theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[50, 30])).
% 4.13/2.89 tff(52,plain,
% 4.13/2.89 ((~![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))) = or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(quant_inst,[status(thm)],[])).
% 4.13/2.89 tff(53,plain,
% 4.13/2.89 (implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))) = or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))),
% 4.13/2.89 inference(unit_resolution,[status(thm)],[52, 22])).
% 4.13/2.89 tff(54,plain,
% 4.13/2.89 (or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))) = implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))),
% 4.13/2.89 inference(symmetry,[status(thm)],[53])).
% 4.13/2.89 tff(55,plain,
% 4.13/2.89 (theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))) <=> theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(monotonicity,[status(thm)],[54])).
% 4.13/2.89 tff(56,plain,
% 4.13/2.89 (theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))) <=> theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(symmetry,[status(thm)],[55])).
% 4.13/2.89 tff(57,plain,
% 4.13/2.89 (^[B: $i, A: $i] : refl(axiom(implies(A, or(B, A))) <=> axiom(implies(A, or(B, A))))),
% 4.13/2.89 inference(bind,[status(th)],[])).
% 4.13/2.89 tff(58,plain,
% 4.13/2.89 (![B: $i, A: $i] : axiom(implies(A, or(B, A))) <=> ![B: $i, A: $i] : axiom(implies(A, or(B, A)))),
% 4.13/2.89 inference(quant_intro,[status(thm)],[57])).
% 4.13/2.89 tff(59,plain,
% 4.13/2.89 (![B: $i, A: $i] : axiom(implies(A, or(B, A))) <=> ![B: $i, A: $i] : axiom(implies(A, or(B, A)))),
% 4.13/2.89 inference(rewrite,[status(thm)],[])).
% 4.13/2.89 tff(60,axiom,(![B: $i, A: $i] : axiom(implies(A, or(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax','axiom_1_3')).
% 4.13/2.89 tff(61,plain,
% 4.13/2.89 (![B: $i, A: $i] : axiom(implies(A, or(B, A)))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[60, 59])).
% 4.13/2.89 tff(62,plain,(
% 4.13/2.89 ![B: $i, A: $i] : axiom(implies(A, or(B, A)))),
% 4.13/2.89 inference(skolemize,[status(sab)],[61])).
% 4.13/2.89 tff(63,plain,
% 4.13/2.89 (![B: $i, A: $i] : axiom(implies(A, or(B, A)))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[62, 58])).
% 4.13/2.89 tff(64,plain,
% 4.13/2.89 ((~![B: $i, A: $i] : axiom(implies(A, or(B, A)))) | axiom(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(quant_inst,[status(thm)],[])).
% 4.13/2.89 tff(65,plain,
% 4.13/2.89 (axiom(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(unit_resolution,[status(thm)],[64, 63])).
% 4.13/2.89 tff(66,plain,
% 4.13/2.89 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))) | (~axiom(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))) | (~axiom(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))))),
% 4.13/2.89 inference(rewrite,[status(thm)],[])).
% 4.13/2.89 tff(67,plain,
% 4.13/2.89 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))) | (~axiom(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))))),
% 4.13/2.89 inference(quant_inst,[status(thm)],[])).
% 4.13/2.89 tff(68,plain,
% 4.13/2.89 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))) | (~axiom(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p))))))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[67, 66])).
% 4.13/2.89 tff(69,plain,
% 4.13/2.89 (theorem(implies(not(or(not(p), not(not(p)))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(unit_resolution,[status(thm)],[68, 46, 65])).
% 4.13/2.89 tff(70,plain,
% 4.13/2.89 (theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[69, 56])).
% 4.13/2.89 tff(71,plain,
% 4.13/2.89 (^[Y: $i, X: $i] : refl((theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X)))) <=> (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X)))))),
% 4.13/2.89 inference(bind,[status(th)],[])).
% 4.13/2.89 tff(72,plain,
% 4.13/2.89 (![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X)))) <=> ![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(quant_intro,[status(thm)],[71])).
% 4.13/2.89 tff(73,plain,
% 4.13/2.89 (![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X)))) <=> ![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(rewrite,[status(thm)],[])).
% 4.13/2.89 tff(74,plain,
% 4.13/2.89 (^[Y: $i, X: $i] : rewrite(((theorem(X) | (~theorem(implies(Y, X)))) | (~theorem(Y))) <=> (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X)))))),
% 4.13/2.89 inference(bind,[status(th)],[])).
% 4.13/2.89 tff(75,plain,
% 4.13/2.89 (![Y: $i, X: $i] : ((theorem(X) | (~theorem(implies(Y, X)))) | (~theorem(Y))) <=> ![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(quant_intro,[status(thm)],[74])).
% 4.13/2.89 tff(76,axiom,(![Y: $i, X: $i] : ((theorem(X) | (~theorem(implies(Y, X)))) | (~theorem(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax','rule_2')).
% 4.13/2.89 tff(77,plain,
% 4.13/2.89 (![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[76, 75])).
% 4.13/2.89 tff(78,plain,
% 4.13/2.89 (![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[77, 73])).
% 4.13/2.89 tff(79,plain,(
% 4.13/2.89 ![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(skolemize,[status(sab)],[78])).
% 4.13/2.89 tff(80,plain,
% 4.13/2.89 (![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))),
% 4.13/2.89 inference(modus_ponens,[status(thm)],[79, 72])).
% 4.13/2.89 tff(81,plain,
% 4.13/2.89 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))))),
% 4.13/2.90 inference(rewrite,[status(thm)],[])).
% 4.13/2.90 tff(82,plain,
% 4.13/2.90 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))))))),
% 4.13/2.90 inference(quant_inst,[status(thm)],[])).
% 4.13/2.90 tff(83,plain,
% 4.13/2.90 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))))),
% 4.13/2.90 inference(modus_ponens,[status(thm)],[82, 81])).
% 4.13/2.90 tff(84,plain,
% 4.13/2.90 (theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p))))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), not(or(not(p), not(not(p)))))), or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))))),
% 4.13/2.90 inference(unit_resolution,[status(thm)],[83, 80])).
% 4.13/2.90 tff(85,plain,
% 4.13/2.90 (theorem(or(not(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))), or(not(and(p, not(p))), not(or(not(p), not(not(p)))))))),
% 4.13/2.90 inference(unit_resolution,[status(thm)],[84, 70, 51])).
% 4.13/2.90 tff(86,plain,
% 4.13/2.90 (theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))),
% 4.13/2.90 inference(modus_ponens,[status(thm)],[85, 27])).
% 4.13/2.90 tff(87,assumption,(~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))), introduced(assumption)).
% 4.13/2.90 tff(88,plain,
% 4.13/2.90 ($false),
% 4.13/2.90 inference(unit_resolution,[status(thm)],[87, 86])).
% 4.13/2.90 tff(89,plain,(theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))), inference(lemma,lemma(discharge,[]))).
% 4.13/2.90 tff(90,plain,
% 4.13/2.90 (implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))) = implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))),
% 4.13/2.90 inference(monotonicity,[status(thm)],[13])).
% 4.13/2.90 tff(91,plain,
% 4.13/2.90 (theorem(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))) <=> theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))),
% 4.13/2.90 inference(monotonicity,[status(thm)],[90])).
% 4.13/2.90 tff(92,plain,
% 4.13/2.90 (^[B: $i, A: $i] : refl(axiom(implies(or(A, B), or(B, A))) <=> axiom(implies(or(A, B), or(B, A))))),
% 4.13/2.90 inference(bind,[status(th)],[])).
% 4.13/2.90 tff(93,plain,
% 4.13/2.90 (![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A))) <=> ![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))),
% 4.13/2.90 inference(quant_intro,[status(thm)],[92])).
% 4.13/2.90 tff(94,plain,
% 4.13/2.90 (![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A))) <=> ![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))),
% 4.13/2.90 inference(rewrite,[status(thm)],[])).
% 4.13/2.90 tff(95,axiom,(![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL004-0.ax','axiom_1_4')).
% 4.13/2.90 tff(96,plain,
% 4.13/2.90 (![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))),
% 4.13/2.90 inference(modus_ponens,[status(thm)],[95, 94])).
% 4.13/2.90 tff(97,plain,(
% 4.13/2.90 ![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))),
% 4.13/2.90 inference(skolemize,[status(sab)],[96])).
% 4.13/2.90 tff(98,plain,
% 4.13/2.90 (![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))),
% 4.13/2.90 inference(modus_ponens,[status(thm)],[97, 93])).
% 4.13/2.90 tff(99,plain,
% 4.13/2.90 ((~![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))) | axiom(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))),
% 4.13/2.90 inference(quant_inst,[status(thm)],[])).
% 4.13/2.90 tff(100,plain,
% 4.13/2.90 (axiom(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))),
% 4.13/2.90 inference(unit_resolution,[status(thm)],[99, 98])).
% 4.13/2.90 tff(101,plain,
% 4.13/2.90 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))) | (~axiom(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))) | (~axiom(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))))),
% 4.13/2.90 inference(rewrite,[status(thm)],[])).
% 4.13/2.90 tff(102,plain,
% 4.13/2.90 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))) | (~axiom(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))))),
% 4.13/2.90 inference(quant_inst,[status(thm)],[])).
% 4.13/2.90 tff(103,plain,
% 4.13/2.90 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))) | (~axiom(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))))),
% 4.13/2.90 inference(modus_ponens,[status(thm)],[102, 101])).
% 4.13/2.90 tff(104,plain,
% 4.13/2.90 (theorem(implies(or(not(and(p, not(p))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))),
% 4.13/2.90 inference(unit_resolution,[status(thm)],[103, 46, 100])).
% 4.13/2.90 tff(105,plain,
% 4.13/2.90 (theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))),
% 4.13/2.90 inference(modus_ponens,[status(thm)],[104, 91])).
% 4.13/2.91 tff(106,plain,
% 4.13/2.91 ((~![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(p), not(not(p))), not(and(p, not(p)))) = or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(107,plain,
% 4.13/2.91 (implies(or(not(p), not(not(p))), not(and(p, not(p)))) = or(not(or(not(p), not(not(p)))), not(and(p, not(p))))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[106, 22])).
% 4.13/2.91 tff(108,plain,
% 4.13/2.91 (theorem(implies(or(not(p), not(not(p))), not(and(p, not(p))))) <=> theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))),
% 4.13/2.91 inference(monotonicity,[status(thm)],[107])).
% 4.13/2.91 tff(109,plain,
% 4.13/2.91 ((~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p)))))) <=> (~theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))),
% 4.13/2.91 inference(monotonicity,[status(thm)],[108])).
% 4.13/2.91 tff(110,plain,
% 4.13/2.91 ((~![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))) | axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(111,plain,
% 4.13/2.91 (axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[110, 98])).
% 4.13/2.91 tff(112,plain,
% 4.13/2.91 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))) | (~axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))) | (~axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))))),
% 4.13/2.91 inference(rewrite,[status(thm)],[])).
% 4.13/2.91 tff(113,plain,
% 4.13/2.91 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))) | (~axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(114,plain,
% 4.13/2.91 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))) | (~axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))))),
% 4.13/2.91 inference(modus_ponens,[status(thm)],[113, 112])).
% 4.13/2.91 tff(115,plain,
% 4.13/2.91 (theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[114, 46, 111])).
% 4.13/2.91 tff(116,plain,
% 4.13/2.91 ((~![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))) = or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(117,plain,
% 4.13/2.91 (implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))) = or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[116, 22])).
% 4.13/2.91 tff(118,plain,
% 4.13/2.91 (theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p)))) <=> theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))),
% 4.13/2.91 inference(monotonicity,[status(thm)],[117])).
% 4.13/2.91 tff(119,plain,
% 4.13/2.91 (theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))) <=> theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))))),
% 4.13/2.91 inference(symmetry,[status(thm)],[118])).
% 4.13/2.91 tff(120,plain,
% 4.13/2.91 ((~![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))) | axiom(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(121,plain,
% 4.13/2.91 (axiom(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[120, 37])).
% 4.13/2.91 tff(122,plain,
% 4.13/2.91 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))) | (~axiom(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))) | (~axiom(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))))),
% 4.13/2.91 inference(rewrite,[status(thm)],[])).
% 4.13/2.91 tff(123,plain,
% 4.13/2.91 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))) | (~axiom(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(124,plain,
% 4.13/2.91 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))) | (~axiom(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))))),
% 4.13/2.91 inference(modus_ponens,[status(thm)],[123, 122])).
% 4.13/2.91 tff(125,plain,
% 4.13/2.91 (theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[124, 46, 121])).
% 4.13/2.91 tff(126,plain,
% 4.13/2.91 ((~![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))) = or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(127,plain,
% 4.13/2.91 (implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))) = or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[126, 22])).
% 4.13/2.91 tff(128,plain,
% 4.13/2.91 (or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))) = implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))),
% 4.13/2.91 inference(symmetry,[status(thm)],[127])).
% 4.13/2.91 tff(129,plain,
% 4.13/2.91 (axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) <=> axiom(implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.13/2.91 inference(monotonicity,[status(thm)],[128])).
% 4.13/2.91 tff(130,plain,
% 4.13/2.91 (axiom(implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) <=> axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.13/2.91 inference(symmetry,[status(thm)],[129])).
% 4.13/2.91 tff(131,plain,
% 4.13/2.91 ((~![B: $i, A: $i] : axiom(implies(A, or(B, A)))) | axiom(implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.13/2.91 inference(quant_inst,[status(thm)],[])).
% 4.13/2.91 tff(132,plain,
% 4.13/2.91 (axiom(implies(not(p), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.13/2.91 inference(unit_resolution,[status(thm)],[131, 63])).
% 4.13/2.91 tff(133,plain,
% 4.13/2.91 (axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.27/2.91 inference(modus_ponens,[status(thm)],[132, 130])).
% 4.27/2.91 tff(134,plain,
% 4.27/2.91 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) | (~axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) | (~axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))))),
% 4.27/2.91 inference(rewrite,[status(thm)],[])).
% 4.27/2.91 tff(135,plain,
% 4.27/2.91 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) | (~axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))))),
% 4.27/2.91 inference(quant_inst,[status(thm)],[])).
% 4.27/2.91 tff(136,plain,
% 4.27/2.91 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) | (~axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))))),
% 4.27/2.91 inference(modus_ponens,[status(thm)],[135, 134])).
% 4.27/2.91 tff(137,plain,
% 4.27/2.91 (theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))) | (~axiom(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p)))))),
% 4.27/2.91 inference(unit_resolution,[status(thm)],[136, 46])).
% 4.27/2.91 tff(138,plain,
% 4.27/2.91 (theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))),
% 4.27/2.91 inference(unit_resolution,[status(thm)],[137, 133])).
% 4.27/2.91 tff(139,plain,
% 4.27/2.91 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))) | (~theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))) | (~theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))))),
% 4.27/2.91 inference(rewrite,[status(thm)],[])).
% 4.27/2.91 tff(140,plain,
% 4.27/2.91 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))) | (~theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))))))),
% 4.27/2.91 inference(quant_inst,[status(thm)],[])).
% 4.27/2.91 tff(141,plain,
% 4.27/2.91 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))) | (~theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))))),
% 4.27/2.91 inference(modus_ponens,[status(thm)],[140, 139])).
% 4.27/2.91 tff(142,plain,
% 4.27/2.91 (theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p)))) | (~theorem(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), not(p))), or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[141, 80])).
% 4.27/2.92 tff(143,plain,
% 4.27/2.92 (theorem(or(not(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[142, 138, 125])).
% 4.27/2.92 tff(144,plain,
% 4.27/2.92 (theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[143, 119])).
% 4.27/2.92 tff(145,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (implies(X, Y) = or(not(X), Y))) | (implies(or(not(p), not(not(p))), or(not(not(p)), not(p))) = or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(146,plain,
% 4.27/2.92 (implies(or(not(p), not(not(p))), or(not(not(p)), not(p))) = or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[145, 22])).
% 4.27/2.92 tff(147,plain,
% 4.27/2.92 (or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))) = implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))),
% 4.27/2.92 inference(symmetry,[status(thm)],[146])).
% 4.27/2.92 tff(148,plain,
% 4.27/2.92 (theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))) <=> theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(monotonicity,[status(thm)],[147])).
% 4.27/2.92 tff(149,plain,
% 4.27/2.92 (theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))) <=> theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(symmetry,[status(thm)],[148])).
% 4.27/2.92 tff(150,plain,
% 4.27/2.92 ((~![B: $i, A: $i] : axiom(implies(or(A, B), or(B, A)))) | axiom(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(151,plain,
% 4.27/2.92 (axiom(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[150, 98])).
% 4.27/2.92 tff(152,plain,
% 4.27/2.92 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))) | (~axiom(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))) | (~axiom(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(153,plain,
% 4.27/2.92 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))) | (~axiom(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(154,plain,
% 4.27/2.92 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))) | (~axiom(implies(or(not(p), not(not(p))), or(not(not(p)), not(p)))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[153, 152])).
% 4.27/2.92 tff(155,plain,
% 4.27/2.92 (theorem(implies(or(not(p), not(not(p))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[154, 46, 151])).
% 4.27/2.92 tff(156,plain,
% 4.27/2.92 (theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[155, 149])).
% 4.27/2.92 tff(157,plain,
% 4.27/2.92 ((~![B: $i, A: $i, C: $i] : axiom(implies(or(A, or(B, C)), or(B, or(A, C))))) | axiom(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(158,plain,
% 4.27/2.92 (axiom(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[157, 37])).
% 4.27/2.92 tff(159,plain,
% 4.27/2.92 (((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~axiom(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))))) <=> ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~axiom(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(160,plain,
% 4.27/2.92 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | (theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~axiom(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(161,plain,
% 4.27/2.92 ((~![X: $i] : (theorem(X) | (~axiom(X)))) | theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~axiom(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[160, 159])).
% 4.27/2.92 tff(162,plain,
% 4.27/2.92 (theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[161, 46, 158])).
% 4.27/2.92 tff(163,plain,
% 4.27/2.92 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(164,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(165,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[164, 163])).
% 4.27/2.92 tff(166,plain,
% 4.27/2.92 (theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p)))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p)))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[165, 80, 162])).
% 4.27/2.92 tff(167,plain,
% 4.27/2.92 (theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[166, 156])).
% 4.27/2.92 tff(168,plain,
% 4.27/2.92 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(p)), not(p))) | (~theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(not(p)), not(p))) | (~theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(169,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(p)), not(p))) | (~theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p))))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(170,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(not(p)), not(p))) | (~theorem(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))))) | (~theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p)))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[169, 168])).
% 4.27/2.92 tff(171,plain,
% 4.27/2.92 (theorem(or(not(not(p)), not(p))) | (~theorem(implies(or(not(not(p)), or(not(or(not(p), not(not(p)))), not(p))), or(not(not(p)), not(p)))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[170, 80, 167])).
% 4.27/2.92 tff(172,plain,
% 4.27/2.92 (theorem(or(not(not(p)), not(p)))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[171, 144])).
% 4.27/2.92 tff(173,plain,
% 4.27/2.92 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(p), not(not(p)))) | (~theorem(or(not(not(p)), not(p)))) | (~theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(p), not(not(p)))) | (~theorem(or(not(not(p)), not(p)))) | (~theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(174,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(p), not(not(p)))) | (~theorem(or(not(not(p)), not(p)))) | (~theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p)))))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(175,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(p), not(not(p)))) | (~theorem(or(not(not(p)), not(p)))) | (~theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[174, 173])).
% 4.27/2.92 tff(176,plain,
% 4.27/2.92 (theorem(or(not(p), not(not(p)))) | (~theorem(or(not(not(p)), not(p)))) | (~theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[175, 80])).
% 4.27/2.92 tff(177,plain,
% 4.27/2.92 (theorem(or(not(p), not(not(p))))),
% 4.27/2.92 inference(unit_resolution,[status(thm)],[176, 172, 115])).
% 4.27/2.92 tff(178,plain,
% 4.27/2.92 ((~theorem(not(and(p, not(p))))) <=> (~theorem(not(and(p, not(p)))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(179,axiom,(~theorem(not(and(p, not(p))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_this')).
% 4.27/2.92 tff(180,plain,
% 4.27/2.92 (~theorem(not(and(p, not(p))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[179, 178])).
% 4.27/2.92 tff(181,plain,
% 4.27/2.92 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(not(and(p, not(p)))) | (~theorem(or(not(p), not(not(p))))) | (~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p)))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(not(and(p, not(p)))) | (~theorem(or(not(p), not(not(p))))) | (~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p)))))))),
% 4.27/2.92 inference(rewrite,[status(thm)],[])).
% 4.27/2.92 tff(182,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(not(and(p, not(p)))) | (~theorem(or(not(p), not(not(p))))) | (~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p)))))))),
% 4.27/2.92 inference(quant_inst,[status(thm)],[])).
% 4.27/2.92 tff(183,plain,
% 4.27/2.92 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(not(and(p, not(p)))) | (~theorem(or(not(p), not(not(p))))) | (~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p))))))),
% 4.27/2.92 inference(modus_ponens,[status(thm)],[182, 181])).
% 4.27/2.92 tff(184,plain,
% 4.27/2.92 ((~theorem(or(not(p), not(not(p))))) | (~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p))))))),
% 4.27/2.93 inference(unit_resolution,[status(thm)],[183, 80, 180])).
% 4.27/2.93 tff(185,plain,
% 4.27/2.93 (~theorem(implies(or(not(p), not(not(p))), not(and(p, not(p)))))),
% 4.27/2.93 inference(unit_resolution,[status(thm)],[184, 177])).
% 4.27/2.93 tff(186,plain,
% 4.27/2.93 (~theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))),
% 4.27/2.93 inference(modus_ponens,[status(thm)],[185, 109])).
% 4.27/2.93 tff(187,plain,
% 4.27/2.93 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))))),
% 4.27/2.93 inference(rewrite,[status(thm)],[])).
% 4.27/2.93 tff(188,plain,
% 4.27/2.93 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p))))))))),
% 4.27/2.93 inference(quant_inst,[status(thm)],[])).
% 4.27/2.93 tff(189,plain,
% 4.27/2.93 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))))),
% 4.27/2.93 inference(modus_ponens,[status(thm)],[188, 187])).
% 4.27/2.93 tff(190,plain,
% 4.27/2.93 (theorem(or(not(or(not(p), not(not(p)))), not(and(p, not(p))))) | (~theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))) | (~theorem(implies(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))), or(not(or(not(p), not(not(p)))), not(and(p, not(p)))))))),
% 4.27/2.93 inference(unit_resolution,[status(thm)],[189, 80])).
% 4.27/2.93 tff(191,plain,
% 4.27/2.93 (~theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))),
% 4.27/2.93 inference(unit_resolution,[status(thm)],[190, 186, 105])).
% 4.27/2.93 tff(192,plain,
% 4.27/2.93 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | ((~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))),
% 4.27/2.93 inference(rewrite,[status(thm)],[])).
% 4.27/2.93 tff(193,plain,
% 4.27/2.93 ((theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))))) <=> ((~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))),
% 4.27/2.93 inference(rewrite,[status(thm)],[])).
% 4.27/2.94 tff(194,plain,
% 4.27/2.94 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | ((~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))))))),
% 4.27/2.94 inference(monotonicity,[status(thm)],[193])).
% 4.27/2.94 tff(195,plain,
% 4.27/2.94 (((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))) <=> ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))),
% 4.27/2.94 inference(transitivity,[status(thm)],[194, 192])).
% 4.27/2.94 tff(196,plain,
% 4.27/2.94 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))))))),
% 4.27/2.94 inference(quant_inst,[status(thm)],[])).
% 4.27/2.94 tff(197,plain,
% 4.27/2.94 ((~![Y: $i, X: $i] : (theorem(X) | (~theorem(Y)) | (~theorem(implies(Y, X))))) | (~theorem(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))))) | theorem(or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p)))))) | (~theorem(implies(or(not(or(not(p), not(not(p)))), or(not(not(p)), not(p))), or(not(not(or(not(p), not(not(p))))), not(or(not(p), not(not(p))))))))),
% 4.27/2.94 inference(modus_ponens,[status(thm)],[196, 195])).
% 4.27/2.94 tff(198,plain,
% 4.27/2.94 ($false),
% 4.27/2.94 inference(unit_resolution,[status(thm)],[197, 80, 156, 191, 89])).
% 4.27/2.94 % SZS output end Proof
%------------------------------------------------------------------------------