%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL234-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 11:49:26 AM UTC 2026
% Result : Unsatisfiable 2.75s 0.79s
% Output : Proof 3.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL234-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 15:29:21 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.75/0.79 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
% 2.75/0.79
% 2.75/0.79 % SZS status Unsatisfiable
% 2.75/0.79
% 3.54/0.81 % SZS output start Proof
% 3.54/0.81 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 3.54/0.81 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 3.54/0.81 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 3.54/0.81 Axiom 4 (axiom_1_2): axiom(implies(or(X, X), X)) = true.
% 3.54/0.81 Axiom 5 (and_defn): and(X, Y) = not(or(not(X), not(Y))).
% 3.54/0.81 Axiom 6 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 3.54/0.81 Axiom 7 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 3.54/0.81 Axiom 8 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 3.54/0.81 Axiom 9 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 3.54/0.81 Axiom 10 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 3.54/0.81
% 3.54/0.81 Goal 1 (prove_this): theorem(implies(p, implies(q, and(p, q)))) = true.
% 3.54/0.81 Proof:
% 3.54/0.81 theorem(implies(p, implies(q, and(p, q))))
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.81 ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true)
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.81 ifeq(true, true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 8 (rule_2) R->L }
% 3.54/0.81 ifeq(ifeq(theorem(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q)))))), true, ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q)))))), true), true, ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 9 (axiom_1_6) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(or(not(p), or(and(p, q), not(q))), or(not(p), implies(q, and(p, q)))))), true, theorem(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q)))))), true), true, ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), or(not(p), implies(q, and(p, q)))))), true, theorem(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q)))))), true), true, ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(axiom(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q)))))), true, theorem(implies(implies(or(and(p, q), not(q)), implies(q, and(p, q))), implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q)))))), true), true, ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 6 (rule_1) }
% 3.54/0.81 ifeq(ifeq(true, true, ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.81 ifeq(ifeq(theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 7 (axiom_1_4) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), not(q)), or(not(q), and(p, q)))), true, theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.81 ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true, theorem(implies(or(and(p, q), not(q)), implies(q, and(p, q)))), true), true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 6 (rule_1) }
% 3.54/0.81 ifeq(ifeq(true, true, theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(true, true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 8 (rule_2) R->L }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(theorem(implies(or(and(p, q), implies(p, not(q))), implies(p, or(and(p, q), not(q))))), true, ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(p, q), implies(p, not(q))), implies(p, or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 10 (axiom_1_5) R->L }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, 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(implies(or(and(p, q), implies(p, not(q))), implies(p, or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), implies(p, not(q))), or(not(p), or(and(p, q), not(q))))), true, theorem(implies(or(and(p, q), implies(p, not(q))), implies(p, or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), implies(p, not(q))), implies(p, or(and(p, q), not(q))))), true, theorem(implies(or(and(p, q), implies(p, not(q))), implies(p, or(and(p, q), not(q))))), true), true, ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.81 = { by axiom 6 (rule_1) }
% 3.54/0.81 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(true, true, ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(theorem(or(and(p, q), implies(p, not(q)))), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(true, true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 8 (rule_2) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q)))), or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))))), true, ifeq(theorem(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q)))), or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))))), true), true, ifeq(theorem(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 10 (axiom_1_5) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q)))), or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))))), true, theorem(implies(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q)))), or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))))), true), true, ifeq(theorem(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 6 (rule_1) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(and(p, q), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 5 (and_defn) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(or(not(p), not(q))), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(or(not(implies(p, not(q))), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 1 (implies_definition) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(theorem(implies(implies(p, not(q)), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(p, not(q)), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 3 (axiom_1_3) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(p, not(q)), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true, theorem(implies(implies(p, not(q)), or(or(and(p, q), implies(p, not(q))), implies(p, not(q))))), true), true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 6 (rule_1) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true, theorem(or(and(p, q), implies(p, not(q)))), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(true, true, ifeq(theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true, theorem(or(and(p, q), implies(p, not(q)))), true), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 6 (rule_1) R->L }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))), or(and(p, q), implies(p, not(q))))), true, theorem(implies(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))), or(and(p, q), implies(p, not(q))))), true), true, ifeq(theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true, theorem(or(and(p, q), implies(p, not(q)))), true), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 4 (axiom_1_2) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))), or(and(p, q), implies(p, not(q))))), true), true, ifeq(theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true, theorem(or(and(p, q), implies(p, not(q)))), true), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(ifeq(theorem(implies(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q)))), or(and(p, q), implies(p, not(q))))), true, ifeq(theorem(or(or(and(p, q), implies(p, not(q))), or(and(p, q), implies(p, not(q))))), true, theorem(or(and(p, q), implies(p, not(q)))), true), true), true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 8 (rule_2) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(ifeq(true, true, theorem(implies(p, or(and(p, q), not(q)))), true), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 2 (ifeq_axiom) }
% 3.54/0.82 ifeq(theorem(implies(implies(p, or(and(p, q), not(q))), implies(p, implies(q, and(p, q))))), true, ifeq(theorem(implies(p, or(and(p, q), not(q)))), true, theorem(implies(p, implies(q, and(p, q)))), true), true)
% 3.54/0.82 = { by axiom 8 (rule_2) }
% 3.54/0.82 true
% 3.54/0.82 % SZS output end Proof
% 3.54/0.82
% 3.54/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------