%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL239-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 11:49:27 AM UTC 2026
% Result : Unsatisfiable 0.96s 0.62s
% Output : Proof 2.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL239-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 15:34:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.96/0.62 Command-line arguments: --no-flatten-goal
% 0.96/0.62
% 0.96/0.62 % SZS status Unsatisfiable
% 0.96/0.62
% 1.53/0.67 % SZS output start Proof
% 1.53/0.67 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 1.53/0.67 Axiom 2 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 1.53/0.67 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.53/0.67 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 1.53/0.67 Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 1.53/0.67 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 1.53/0.67 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 1.53/0.67 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 1.53/0.67 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 1.53/0.67
% 1.53/0.67 Goal 1 (prove_this): theorem(not(and(p, not(p)))) = true.
% 1.53/0.67 Proof:
% 1.53/0.67 theorem(not(and(p, not(p))))
% 1.53/0.67 = { by axiom 2 (and_defn) }
% 1.53/0.67 theorem(not(not(or(not(p), not(not(p))))))
% 1.53/0.67 = { by axiom 1 (implies_definition) R->L }
% 1.53/0.67 theorem(not(not(implies(p, not(not(p))))))
% 1.53/0.67 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.67 ifeq(true, true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 9 (rule_2) R->L }
% 1.53/0.67 ifeq(ifeq(theorem(implies(implies(not(p), not(p)), or(not(p), not(not(p))))), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 1 (implies_definition) }
% 1.53/0.67 ifeq(ifeq(theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.67 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 7 (axiom_1_4) R->L }
% 1.53/0.67 ifeq(ifeq(ifeq(axiom(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true, theorem(implies(or(not(not(p)), not(p)), or(not(p), not(not(p))))), true), true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 6 (rule_1) }
% 1.53/0.67 ifeq(ifeq(true, true, ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 3 (ifeq_axiom) }
% 1.53/0.67 ifeq(ifeq(theorem(implies(not(p), not(p))), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.67 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.68 ifeq(ifeq(ifeq(true, true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 9 (rule_2) R->L }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(theorem(implies(not(p), or(implies(not(p), not(p)), not(p)))), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(ifeq(true, true, theorem(implies(not(p), or(implies(not(p), not(p)), not(p)))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 4 (axiom_1_3) R->L }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(ifeq(axiom(implies(not(p), or(implies(not(p), not(p)), not(p)))), true, theorem(implies(not(p), or(implies(not(p), not(p)), not(p)))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 6 (rule_1) }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, ifeq(true, true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 3 (ifeq_axiom) }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.68 = { by axiom 8 (axiom_1_5) R->L }
% 1.53/0.68 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(p)), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), or(not(not(p)), not(p))))), true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 1 (implies_definition) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), or(not(not(p)), not(p))))), true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 1 (implies_definition) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true, theorem(implies(implies(not(p), or(implies(not(p), not(p)), not(p))), or(implies(not(p), not(p)), implies(not(p), not(p))))), true), true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 6 (rule_1) }
% 1.53/0.69 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.53/0.69 ifeq(ifeq(ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 6 (rule_1) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true, theorem(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true), true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 5 (axiom_1_2) }
% 1.53/0.69 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true), true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.53/0.69 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(p), not(p)), implies(not(p), not(p))), implies(not(p), not(p)))), true, ifeq(theorem(or(implies(not(p), not(p)), implies(not(p), not(p)))), true, theorem(implies(not(p), not(p))), true), true), true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 9 (rule_2) }
% 1.53/0.69 ifeq(ifeq(true, true, theorem(or(not(p), not(not(p)))), true), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.53/0.69 ifeq(theorem(or(not(p), not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 1 (implies_definition) R->L }
% 1.53/0.69 ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.69 ifeq(true, true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 9 (rule_2) R->L }
% 1.53/0.69 ifeq(ifeq(theorem(implies(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p)))))))), true, ifeq(theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 1 (implies_definition) }
% 1.53/0.69 ifeq(ifeq(theorem(implies(or(not(not(implies(p, not(not(p))))), not(implies(p, not(not(p))))), or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p)))))))), true, ifeq(theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(not(implies(p, not(not(p))))), not(implies(p, not(not(p))))), or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p)))))))), true), true, ifeq(theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 7 (axiom_1_4) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, not(not(p))))), not(implies(p, not(not(p))))), or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p)))))))), true, theorem(implies(or(not(not(implies(p, not(not(p))))), not(implies(p, not(not(p))))), or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p)))))))), true), true, ifeq(theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 6 (rule_1) }
% 1.53/0.69 ifeq(ifeq(true, true, ifeq(theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) }
% 1.53/0.69 ifeq(ifeq(theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 9 (rule_2) R->L }
% 1.53/0.69 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true, ifeq(theorem(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p))))))), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.69 = { by axiom 3 (ifeq_axiom) R->L }
% 1.53/0.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true, ifeq(ifeq(true, true, theorem(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p))))))), true), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.70 = { by axiom 4 (axiom_1_3) R->L }
% 1.53/0.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true, ifeq(ifeq(axiom(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p))))))), true, theorem(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p))))))), true), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.70 = { by axiom 6 (rule_1) }
% 1.53/0.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true, ifeq(true, true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 1.53/0.70 = { by axiom 3 (ifeq_axiom) }
% 2.02/0.70 ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.70 = { by axiom 3 (ifeq_axiom) R->L }
% 2.02/0.70 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.70 = { by axiom 8 (axiom_1_5) R->L }
% 2.02/0.70 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(implies(p, not(not(p))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), or(not(not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))))), true, theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.70 = { by axiom 1 (implies_definition) R->L }
% 2.02/0.70 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), or(not(not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))))), true, theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 1 (implies_definition) R->L }
% 2.02/0.71 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true, theorem(implies(implies(not(implies(p, not(not(p)))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), not(implies(p, not(not(p)))))), or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))))), true), true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 6 (rule_1) }
% 2.02/0.71 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 3 (ifeq_axiom) }
% 2.02/0.71 ifeq(ifeq(ifeq(theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 3 (ifeq_axiom) R->L }
% 2.02/0.71 ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 6 (rule_1) R->L }
% 2.02/0.71 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, theorem(implies(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 5 (axiom_1_2) }
% 2.02/0.71 ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true), true, ifeq(theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 3 (ifeq_axiom) }
% 2.02/0.71 ifeq(ifeq(ifeq(theorem(implies(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, ifeq(theorem(or(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))), implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p))))))), true, theorem(implies(not(implies(p, not(not(p)))), not(implies(p, not(not(p)))))), true), true), true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 9 (rule_2) }
% 2.02/0.71 ifeq(ifeq(true, true, theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 3 (ifeq_axiom) }
% 2.02/0.71 ifeq(theorem(or(not(implies(p, not(not(p)))), not(not(implies(p, not(not(p))))))), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 1 (implies_definition) R->L }
% 2.02/0.71 ifeq(theorem(implies(implies(p, not(not(p))), not(not(implies(p, not(not(p))))))), true, ifeq(theorem(implies(p, not(not(p)))), true, theorem(not(not(implies(p, not(not(p)))))), true), true)
% 2.02/0.71 = { by axiom 9 (rule_2) }
% 2.02/0.71 true
% 2.02/0.71 % SZS output end Proof
% 2.02/0.71
% 2.02/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------