TSTP Solution File: LCL203-10 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LCL203-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n018.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 : Thu Aug 31 08:17:58 EDT 2023
% Result : Unsatisfiable 23.85s 3.52s
% Output : Proof 23.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL203-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 03:12:28 EDT 2023
% 0.14/0.36 % CPUTime :
% 23.85/3.52 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 23.85/3.52
% 23.85/3.52 % SZS status Unsatisfiable
% 23.85/3.52
% 23.85/3.55 % SZS output start Proof
% 23.85/3.55 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 23.85/3.55 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 23.85/3.55 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 23.85/3.55 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 23.85/3.55 Axiom 5 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 23.85/3.55 Axiom 6 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 23.85/3.55 Axiom 7 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 23.85/3.55 Axiom 8 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 23.85/3.55 Axiom 9 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 23.85/3.55
% 23.85/3.55 Lemma 10: theorem(implies(or(X, Y), or(Y, X))) = true.
% 23.85/3.55 Proof:
% 23.85/3.55 theorem(implies(or(X, Y), or(Y, X)))
% 23.85/3.55 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.55 ifeq(true, true, theorem(implies(or(X, Y), or(Y, X))), true)
% 23.85/3.55 = { by axiom 6 (axiom_1_4) R->L }
% 23.85/3.55 ifeq(axiom(implies(or(X, Y), or(Y, X))), true, theorem(implies(or(X, Y), or(Y, X))), true)
% 23.85/3.55 = { by axiom 5 (rule_1) }
% 23.85/3.55 true
% 23.85/3.55
% 23.85/3.55 Lemma 11: ifeq(theorem(implies(implies(X, or(Y, X)), Z)), true, theorem(Z), true) = true.
% 23.85/3.55 Proof:
% 23.85/3.55 ifeq(theorem(implies(implies(X, or(Y, X)), Z)), true, theorem(Z), true)
% 23.85/3.55 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.55 ifeq(theorem(implies(implies(X, or(Y, X)), Z)), true, ifeq(true, true, theorem(Z), true), true)
% 23.85/3.55 = { by axiom 5 (rule_1) R->L }
% 23.85/3.55 ifeq(theorem(implies(implies(X, or(Y, X)), Z)), true, ifeq(ifeq(axiom(implies(X, or(Y, X))), true, theorem(implies(X, or(Y, X))), true), true, theorem(Z), true), true)
% 23.85/3.55 = { by axiom 3 (axiom_1_3) }
% 23.85/3.55 ifeq(theorem(implies(implies(X, or(Y, X)), Z)), true, ifeq(ifeq(true, true, theorem(implies(X, or(Y, X))), true), true, theorem(Z), true), true)
% 23.85/3.55 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.55 ifeq(theorem(implies(implies(X, or(Y, X)), Z)), true, ifeq(theorem(implies(X, or(Y, X))), true, theorem(Z), true), true)
% 23.85/3.55 = { by axiom 9 (rule_2) }
% 23.85/3.56 true
% 23.85/3.56
% 23.85/3.56 Goal 1 (prove_this): theorem(implies(not(or(p, q)), or(not(p), not(q)))) = true.
% 23.85/3.56 Proof:
% 23.85/3.56 theorem(implies(not(or(p, q)), or(not(p), not(q))))
% 23.85/3.56 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.56 ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true)
% 23.85/3.56 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.56 ifeq(true, true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by lemma 11 R->L }
% 23.85/3.56 ifeq(ifeq(theorem(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q)))))), true, theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.56 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q)))))), true), true, theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 7 (axiom_1_6) R->L }
% 23.85/3.56 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(p), not(q))), implies(or(not(not(or(p, q))), not(q)), or(not(not(or(p, q))), or(not(p), not(q)))))), true, theorem(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q)))))), true), true, theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 1 (implies_definition) R->L }
% 23.85/3.56 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), or(not(not(or(p, q))), or(not(p), not(q)))))), true, theorem(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q)))))), true), true, theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 1 (implies_definition) R->L }
% 23.85/3.56 ifeq(ifeq(ifeq(axiom(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q)))))), true, theorem(implies(implies(not(q), or(not(p), not(q))), implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q)))))), true), true, theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 5 (rule_1) }
% 23.85/3.56 ifeq(ifeq(true, true, theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.56 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(true, true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 9 (rule_2) R->L }
% 23.85/3.56 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(theorem(implies(or(not(q), not(not(or(p, q)))), or(not(not(or(p, q))), not(q)))), true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by lemma 10 }
% 23.85/3.56 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.56 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(theorem(or(not(q), not(not(or(p, q))))), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.56 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.56 = { by axiom 9 (rule_2) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(p, q)), not(not(or(p, q)))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 1 (implies_definition) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(or(p, q), not(not(or(p, q)))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(p, q), not(not(or(p, q)))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 7 (axiom_1_6) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(p, q), not(not(or(p, q)))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true, theorem(implies(implies(or(p, q), not(not(or(p, q)))), implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q))))))), true), true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 5 (rule_1) }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(p, q)), not(not(or(p, q))))), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 9 (rule_2) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))), implies(not(or(p, q)), not(or(p, q))))), true, ifeq(theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))), implies(not(or(p, q)), not(or(p, q))))), true), true, ifeq(theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.57 = { by axiom 4 (axiom_1_2) R->L }
% 23.85/3.57 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))), implies(not(or(p, q)), not(or(p, q))))), true, theorem(implies(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))), implies(not(or(p, q)), not(or(p, q))))), true), true, ifeq(theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 5 (rule_1) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 5 (rule_1) R->L }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))))), true, theorem(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))))), true), true, theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 1 (implies_definition) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true, theorem(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))))), true), true, theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 1 (implies_definition) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(not(or(p, q))), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), or(not(not(or(p, q))), not(or(p, q)))))), true, theorem(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))))), true), true, theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 8 (axiom_1_5) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))))), true), true, theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(or(p, q)), or(implies(not(or(p, q)), not(or(p, q))), not(or(p, q)))), or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q)))))), true, theorem(or(implies(not(or(p, q)), not(or(p, q))), implies(not(or(p, q)), not(or(p, q))))), true), true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by lemma 11 }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(not(or(p, q)), not(or(p, q)))), true), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(not(or(p, q)), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(implies(not(or(p, q)), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by lemma 10 R->L }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(not(or(p, q))), not(or(p, q))), or(not(or(p, q)), not(not(or(p, q)))))), true, ifeq(theorem(implies(not(or(p, q)), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 1 (implies_definition) R->L }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(not(or(p, q)), not(or(p, q))), or(not(or(p, q)), not(not(or(p, q)))))), true, ifeq(theorem(implies(not(or(p, q)), not(or(p, q)))), true, theorem(or(not(or(p, q)), not(not(or(p, q))))), true), true), true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 9 (rule_2) }
% 23.85/3.58 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.58 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true, theorem(or(not(q), not(not(or(p, q))))), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 2 (ifeq_axiom) R->L }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true, ifeq(true, true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 5 (rule_1) R->L }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true, ifeq(ifeq(axiom(implies(q, or(p, q))), true, theorem(implies(q, or(p, q))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 3 (axiom_1_3) }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true, ifeq(ifeq(true, true, theorem(implies(q, or(p, q))), true), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true, ifeq(theorem(implies(q, or(p, q))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 1 (implies_definition) }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(not(q), or(p, q)), or(not(q), not(not(or(p, q)))))), true, ifeq(theorem(or(not(q), or(p, q))), true, theorem(or(not(q), not(not(or(p, q))))), true), true), true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 9 (rule_2) }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(ifeq(true, true, theorem(or(not(not(or(p, q))), not(q))), true), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 2 (ifeq_axiom) }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(theorem(or(not(not(or(p, q))), not(q))), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 1 (implies_definition) R->L }
% 23.85/3.59 ifeq(theorem(implies(implies(not(or(p, q)), not(q)), implies(not(or(p, q)), or(not(p), not(q))))), true, ifeq(theorem(implies(not(or(p, q)), not(q))), true, theorem(implies(not(or(p, q)), or(not(p), not(q)))), true), true)
% 23.85/3.59 = { by axiom 9 (rule_2) }
% 23.85/3.59 true
% 23.85/3.59 % SZS output end Proof
% 23.85/3.59
% 23.85/3.59 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------