%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL311-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Tue Sep 29 11:49:35 AM UTC 2026
% Result : Unsatisfiable 14.32s 2.32s
% Output : Proof 15.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL311-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n011.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 27 15:34:15 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.32/2.32 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 14.32/2.32
% 14.32/2.32 % SZS status Unsatisfiable
% 14.32/2.32
% 15.10/2.42 % SZS output start Proof
% 15.10/2.42 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 15.10/2.42 Axiom 2 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 15.10/2.42 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 15.10/2.42 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 15.10/2.42 Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 15.10/2.42 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 15.10/2.42 Axiom 7 (equivalent_defn): equivalent(X, Y) = and(implies(X, Y), implies(Y, X)).
% 15.10/2.42 Axiom 8 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 15.10/2.42 Axiom 9 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 15.10/2.42 Axiom 10 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 15.10/2.42
% 15.10/2.43 Lemma 11: not(implies(X, not(Y))) = and(X, Y).
% 15.10/2.43 Proof:
% 15.10/2.43 not(implies(X, not(Y)))
% 15.10/2.43 = { by axiom 1 (implies_definition) }
% 15.10/2.43 not(or(not(X), not(Y)))
% 15.10/2.43 = { by axiom 2 (and_defn) R->L }
% 15.10/2.43 and(X, Y)
% 15.10/2.43
% 15.10/2.43 Goal 1 (prove_this): theorem(equivalent(implies(p, not(p)), not(p))) = true.
% 15.10/2.43 Proof:
% 15.10/2.43 theorem(equivalent(implies(p, not(p)), not(p)))
% 15.10/2.43 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.43 ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true)
% 15.10/2.43 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.43 ifeq(true, true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.43 = { by axiom 10 (rule_2) R->L }
% 15.10/2.43 ifeq(ifeq(theorem(implies(implies(implies(p, not(p)), not(p)), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, ifeq(theorem(implies(implies(p, not(p)), not(p))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.43 = { by axiom 1 (implies_definition) }
% 15.10/2.43 ifeq(ifeq(theorem(implies(implies(implies(p, not(p)), not(p)), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, ifeq(theorem(implies(or(not(p), not(p)), not(p))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.43 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.43 ifeq(ifeq(theorem(implies(implies(implies(p, not(p)), not(p)), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, ifeq(ifeq(true, true, theorem(implies(or(not(p), not(p)), not(p))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.44 = { by axiom 5 (axiom_1_2) R->L }
% 15.10/2.44 ifeq(ifeq(theorem(implies(implies(implies(p, not(p)), not(p)), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, ifeq(ifeq(axiom(implies(or(not(p), not(p)), not(p))), true, theorem(implies(or(not(p), not(p)), not(p))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.44 = { by axiom 6 (rule_1) }
% 15.10/2.44 ifeq(ifeq(theorem(implies(implies(implies(p, not(p)), not(p)), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, ifeq(true, true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.44 = { by axiom 3 (ifeq_axiom) }
% 15.10/2.44 ifeq(ifeq(theorem(implies(implies(implies(p, not(p)), not(p)), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.44 = { by axiom 1 (implies_definition) }
% 15.10/2.44 ifeq(ifeq(theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.44 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.44 ifeq(ifeq(ifeq(true, true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.44 = { by axiom 6 (rule_1) R->L }
% 15.10/2.45 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.45 = { by axiom 1 (implies_definition) }
% 15.10/2.45 ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), or(not(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p))))), equivalent(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.45 = { by axiom 1 (implies_definition) }
% 15.10/2.45 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p))))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), or(not(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p))))), equivalent(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.45 = { by axiom 9 (axiom_1_5) }
% 15.10/2.46 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.46 = { by axiom 3 (ifeq_axiom) }
% 15.10/2.46 ifeq(ifeq(ifeq(theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.46 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.46 ifeq(ifeq(ifeq(theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true, ifeq(true, true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.46 = { by axiom 6 (rule_1) R->L }
% 15.10/2.46 ifeq(ifeq(ifeq(theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true, ifeq(ifeq(axiom(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p))))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.46 = { by axiom 8 (axiom_1_4) }
% 15.10/2.47 ifeq(ifeq(ifeq(theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true, ifeq(ifeq(true, true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p))))), true), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by axiom 3 (ifeq_axiom) }
% 15.10/2.47 ifeq(ifeq(ifeq(theorem(implies(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))))), true, ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), or(not(implies(implies(p, not(p)), not(p))), equivalent(implies(p, not(p)), not(p))))), true, theorem(or(not(implies(implies(p, not(p)), not(p))), implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p))))), true), true), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by axiom 10 (rule_2) }
% 15.10/2.47 ifeq(ifeq(true, true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by axiom 3 (ifeq_axiom) }
% 15.10/2.47 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), not(implies(implies(p, not(p)), not(p)))), equivalent(implies(p, not(p)), not(p)))), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by lemma 11 }
% 15.10/2.47 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(true, true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by axiom 10 (rule_2) R->L }
% 15.10/2.47 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.47 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.47 = { by axiom 6 (rule_1) R->L }
% 15.10/2.47 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(implies(p, not(p)), not(p))), not(implies(not(p), implies(p, not(p))))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(or(not(implies(implies(p, not(p)), not(p))), not(implies(not(p), implies(p, not(p))))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.48 = { by axiom 8 (axiom_1_4) }
% 15.10/2.48 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(implies(implies(p, not(p)), not(p))), not(implies(not(p), implies(p, not(p))))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.48 = { by axiom 3 (ifeq_axiom) }
% 15.10/2.48 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(implies(implies(p, not(p)), not(p))), not(implies(not(p), implies(p, not(p))))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.48 = { by axiom 1 (implies_definition) R->L }
% 15.10/2.48 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, not(p)), not(p)), not(implies(not(p), implies(p, not(p))))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.48 = { by axiom 1 (implies_definition) }
% 15.10/2.48 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(or(not(implies(implies(implies(p, not(p)), not(p)), not(implies(not(p), implies(p, not(p)))))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.48 = { by lemma 11 }
% 15.10/2.48 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(or(and(implies(implies(p, not(p)), not(p)), implies(not(p), implies(p, not(p)))), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.49 = { by axiom 7 (equivalent_defn) R->L }
% 15.10/2.49 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), or(not(implies(not(p), implies(p, not(p)))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.49 = { by axiom 1 (implies_definition) R->L }
% 15.10/2.49 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), not(implies(implies(p, not(p)), not(p)))))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.49 = { by lemma 11 }
% 15.10/2.49 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.49 = { by axiom 3 (ifeq_axiom) R->L }
% 15.10/2.49 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.49 = { by axiom 6 (rule_1) R->L }
% 15.10/2.50 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true), true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.50 = { by axiom 1 (implies_definition) }
% 15.10/2.50 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), or(not(implies(not(p), implies(p, not(p)))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true), true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.10/2.50 = { by axiom 1 (implies_definition) }
% 15.10/2.50 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(equivalent(implies(p, not(p)), not(p)), or(not(implies(not(p), implies(p, not(p)))), and(implies(p, not(p)), p))), or(not(implies(not(p), implies(p, not(p)))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true), true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.50 = { by axiom 9 (axiom_1_5) }
% 15.90/2.50 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true), true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.50 = { by axiom 3 (ifeq_axiom) }
% 15.90/2.50 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p))), implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))))), true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), implies(implies(not(p), implies(p, not(p))), and(implies(p, not(p)), p)))), true, theorem(implies(implies(not(p), implies(p, not(p))), or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)))), true), true), true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 10 (rule_2) }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(true, true, ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 3 (ifeq_axiom) }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(theorem(implies(not(p), implies(p, not(p)))), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 3 (ifeq_axiom) R->L }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(not(p), implies(p, not(p)))), true), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 4 (axiom_1_3) R->L }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(axiom(implies(not(p), or(not(p), not(p)))), true, theorem(implies(not(p), implies(p, not(p)))), true), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 1 (implies_definition) R->L }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(ifeq(axiom(implies(not(p), implies(p, not(p)))), true, theorem(implies(not(p), implies(p, not(p)))), true), true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 6 (rule_1) }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(ifeq(true, true, theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 3 (ifeq_axiom) }
% 15.90/2.51 ifeq(theorem(implies(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p)), equivalent(implies(p, not(p)), not(p)))), true, ifeq(theorem(or(equivalent(implies(p, not(p)), not(p)), and(implies(p, not(p)), p))), true, theorem(equivalent(implies(p, not(p)), not(p))), true), true)
% 15.90/2.51 = { by axiom 10 (rule_2) }
% 15.90/2.51 true
% 15.90/2.51 % SZS output end Proof
% 15.90/2.51
% 15.90/2.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------