%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL261-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 11:49:30 AM UTC 2026
% Result : Unsatisfiable 25.94s 3.86s
% Output : Proof 27.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL261-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.07 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n020.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 27 15:32:34 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.94/3.86 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 25.94/3.86
% 25.94/3.86 % SZS status Unsatisfiable
% 25.94/3.86
% 26.72/3.96 % SZS output start Proof
% 26.72/3.96 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 26.72/3.96 Axiom 2 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 26.72/3.96 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 26.72/3.96 Axiom 4 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 26.72/3.96 Axiom 5 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 26.72/3.96 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 26.72/3.96 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 26.72/3.96 Axiom 8 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 26.72/3.96 Axiom 9 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 26.72/3.96 Axiom 10 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 26.72/3.96
% 26.72/3.96 Goal 1 (prove_this): theorem(or(not(p), or(not(q), and(p, q)))) = true.
% 26.72/3.96 Proof:
% 26.72/3.96 theorem(or(not(p), or(not(q), and(p, q))))
% 26.72/3.96 = { by axiom 3 (ifeq_axiom) R->L }
% 26.72/3.96 ifeq(true, true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.96 = { by axiom 10 (rule_2) R->L }
% 26.72/3.96 ifeq(ifeq(theorem(implies(or(and(p, q), or(not(p), not(q))), or(not(p), or(and(p, q), not(q))))), true, ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 1 (implies_definition) }
% 26.72/3.97 ifeq(ifeq(theorem(or(not(or(and(p, q), or(not(p), not(q)))), or(not(p), or(and(p, q), not(q))))), true, ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 3 (ifeq_axiom) R->L }
% 26.72/3.97 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(and(p, q), or(not(p), not(q)))), or(not(p), or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 9 (axiom_1_5) R->L }
% 26.72/3.97 ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), or(not(p), not(q))), or(not(p), or(and(p, q), not(q))))), true, theorem(or(not(or(and(p, q), or(not(p), not(q)))), or(not(p), or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 1 (implies_definition) }
% 26.72/3.97 ifeq(ifeq(ifeq(axiom(or(not(or(and(p, q), or(not(p), not(q)))), or(not(p), or(and(p, q), not(q))))), true, theorem(or(not(or(and(p, q), or(not(p), not(q)))), or(not(p), or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 6 (rule_1) }
% 26.72/3.97 ifeq(ifeq(true, true, ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 3 (ifeq_axiom) }
% 26.72/3.97 ifeq(ifeq(theorem(or(and(p, q), or(not(p), not(q)))), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 3 (ifeq_axiom) R->L }
% 26.72/3.97 ifeq(ifeq(ifeq(true, true, theorem(or(and(p, q), or(not(p), not(q)))), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 6 (rule_1) R->L }
% 26.72/3.97 ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(p), not(q))), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(not(or(not(p), not(q))), or(or(not(p), not(q)), or(not(p), not(q))))), true), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 1 (implies_definition) R->L }
% 26.72/3.97 ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(p), not(q)), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(not(or(not(p), not(q))), or(or(not(p), not(q)), or(not(p), not(q))))), true), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 4 (axiom_1_3) }
% 26.72/3.97 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(p), not(q))), or(or(not(p), not(q)), or(not(p), not(q))))), true), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 3 (ifeq_axiom) }
% 26.72/3.97 ifeq(ifeq(ifeq(theorem(or(not(or(not(p), not(q))), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.97 = { by axiom 2 (and_defn) R->L }
% 26.72/3.97 ifeq(ifeq(ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.98 = { by axiom 3 (ifeq_axiom) R->L }
% 26.72/3.98 ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.98 = { by axiom 10 (rule_2) R->L }
% 26.72/3.98 ifeq(ifeq(ifeq(ifeq(theorem(implies(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, ifeq(theorem(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.98 = { by axiom 1 (implies_definition) }
% 26.72/3.98 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, ifeq(theorem(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.98 = { by axiom 3 (ifeq_axiom) R->L }
% 26.72/3.98 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, ifeq(ifeq(true, true, theorem(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.99 = { by axiom 5 (axiom_1_2) R->L }
% 26.72/3.99 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, ifeq(ifeq(axiom(implies(or(or(not(p), not(q)), or(not(p), not(q))), or(not(p), not(q)))), true, theorem(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.99 = { by axiom 1 (implies_definition) }
% 26.72/3.99 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, ifeq(ifeq(axiom(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), true, theorem(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.99 = { by axiom 6 (rule_1) }
% 26.72/3.99 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, ifeq(true, true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.99 = { by axiom 3 (ifeq_axiom) }
% 26.72/3.99 ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/3.99 = { by axiom 3 (ifeq_axiom) R->L }
% 26.72/3.99 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/4.00 = { by axiom 8 (axiom_1_6) R->L }
% 26.72/4.00 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(or(or(not(p), not(q)), or(not(p), not(q))), or(not(p), not(q))), implies(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q)))), or(and(p, q), or(not(p), not(q)))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 26.72/4.00 = { by axiom 1 (implies_definition) }
% 26.72/4.00 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(implies(or(or(not(p), not(q)), or(not(p), not(q))), or(not(p), not(q)))), implies(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q)))), or(and(p, q), or(not(p), not(q)))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.00 = { by axiom 1 (implies_definition) }
% 27.47/4.00 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), implies(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q)))), or(and(p, q), or(not(p), not(q)))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.00 = { by axiom 1 (implies_definition) }
% 27.47/4.00 ifeq(ifeq(ifeq(ifeq(ifeq(axiom(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true, theorem(or(not(or(not(or(or(not(p), not(q)), or(not(p), not(q)))), or(not(p), not(q)))), or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q)))))), true), true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.00 = { by axiom 6 (rule_1) }
% 27.47/4.00 ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.00 = { by axiom 3 (ifeq_axiom) }
% 27.47/4.00 ifeq(ifeq(ifeq(theorem(or(not(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), or(and(p, q), or(not(p), not(q))))), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.01 = { by axiom 1 (implies_definition) R->L }
% 27.47/4.01 ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q)))), or(and(p, q), or(not(p), not(q))))), true, ifeq(theorem(or(and(p, q), or(or(not(p), not(q)), or(not(p), not(q))))), true, theorem(or(and(p, q), or(not(p), not(q)))), true), true), true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.01 = { by axiom 10 (rule_2) }
% 27.47/4.01 ifeq(ifeq(true, true, theorem(or(not(p), or(and(p, q), not(q)))), true), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.01 = { by axiom 3 (ifeq_axiom) }
% 27.47/4.01 ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true)
% 27.47/4.01 = { by axiom 3 (ifeq_axiom) R->L }
% 27.47/4.01 ifeq(true, true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.01 = { by axiom 10 (rule_2) R->L }
% 27.47/4.01 ifeq(ifeq(theorem(implies(or(not(or(and(p, q), not(q))), or(not(q), and(p, q))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, ifeq(theorem(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.01 = { by axiom 1 (implies_definition) }
% 27.47/4.01 ifeq(ifeq(theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, ifeq(theorem(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.01 = { by axiom 3 (ifeq_axiom) R->L }
% 27.47/4.01 ifeq(ifeq(theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, ifeq(ifeq(true, true, theorem(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.01 = { by axiom 7 (axiom_1_4) R->L }
% 27.47/4.01 ifeq(ifeq(theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, ifeq(ifeq(axiom(implies(or(and(p, q), not(q)), or(not(q), and(p, q)))), true, theorem(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.01 = { by axiom 1 (implies_definition) }
% 27.47/4.01 ifeq(ifeq(theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, ifeq(ifeq(axiom(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), true, theorem(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 6 (rule_1) }
% 27.47/4.02 ifeq(ifeq(theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, ifeq(true, true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 3 (ifeq_axiom) }
% 27.47/4.02 ifeq(ifeq(theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 3 (ifeq_axiom) R->L }
% 27.47/4.02 ifeq(ifeq(ifeq(true, true, theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 8 (axiom_1_6) R->L }
% 27.47/4.02 ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), not(q)), or(not(q), and(p, q))), implies(or(not(p), or(and(p, q), not(q))), or(not(p), or(not(q), and(p, q)))))), true, theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 1 (implies_definition) }
% 27.47/4.02 ifeq(ifeq(ifeq(axiom(or(not(implies(or(and(p, q), not(q)), or(not(q), and(p, q)))), implies(or(not(p), or(and(p, q), not(q))), or(not(p), or(not(q), and(p, q)))))), true, theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 1 (implies_definition) }
% 27.47/4.02 ifeq(ifeq(ifeq(axiom(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), implies(or(not(p), or(and(p, q), not(q))), or(not(p), or(not(q), and(p, q)))))), true, theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 1 (implies_definition) }
% 27.47/4.02 ifeq(ifeq(ifeq(axiom(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true, theorem(or(not(or(not(or(and(p, q), not(q))), or(not(q), and(p, q)))), or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q)))))), true), true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 6 (rule_1) }
% 27.47/4.02 ifeq(ifeq(true, true, theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 3 (ifeq_axiom) }
% 27.47/4.02 ifeq(theorem(or(not(or(not(p), or(and(p, q), not(q)))), or(not(p), or(not(q), and(p, q))))), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 1 (implies_definition) R->L }
% 27.47/4.02 ifeq(theorem(implies(or(not(p), or(and(p, q), not(q))), or(not(p), or(not(q), and(p, q))))), true, ifeq(theorem(or(not(p), or(and(p, q), not(q)))), true, theorem(or(not(p), or(not(q), and(p, q)))), true), true)
% 27.47/4.02 = { by axiom 10 (rule_2) }
% 27.47/4.02 true
% 27.47/4.02 % SZS output end Proof
% 27.47/4.02
% 27.47/4.02 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------