%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL190-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 11:49:16 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL190-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.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 15:25:31 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 Command-line arguments: --flatten --complete-subsets
% 0.18/0.47
% 0.18/0.47 % SZS status Unsatisfiable
% 0.18/0.47
% 0.18/0.47 % SZS output start Proof
% 0.18/0.47 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.18/0.47 Axiom 2 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 0.18/0.47 Axiom 3 (axiom_1_4): axiom(implies(or(X, Y), or(Y, X))) = true.
% 0.18/0.47 Axiom 4 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 0.18/0.47 Axiom 5 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 0.18/0.47
% 0.18/0.47 Goal 1 (prove_this): theorem(implies(or(p, or(q, r)), or(p, or(r, q)))) = true.
% 0.18/0.47 Proof:
% 0.18/0.47 theorem(implies(or(p, or(q, r)), or(p, or(r, q))))
% 0.18/0.47 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.47 ifeq(true, true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true)
% 0.18/0.47 = { by axiom 2 (rule_1) R->L }
% 0.18/0.47 ifeq(ifeq(axiom(implies(or(q, r), or(r, q))), true, theorem(implies(or(q, r), or(r, q))), true), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true)
% 0.18/0.47 = { by axiom 3 (axiom_1_4) }
% 0.18/0.48 ifeq(ifeq(true, true, theorem(implies(or(q, r), or(r, q))), true), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true)
% 0.18/0.48 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.48 ifeq(theorem(implies(or(q, r), or(r, q))), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true)
% 0.18/0.48 = { by axiom 1 (ifeq_axiom) R->L }
% 0.18/0.48 ifeq(true, true, ifeq(theorem(implies(or(q, r), or(r, q))), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true), true)
% 0.18/0.48 = { by axiom 2 (rule_1) R->L }
% 0.18/0.48 ifeq(ifeq(axiom(implies(implies(or(q, r), or(r, q)), implies(or(p, or(q, r)), or(p, or(r, q))))), true, theorem(implies(implies(or(q, r), or(r, q)), implies(or(p, or(q, r)), or(p, or(r, q))))), true), true, ifeq(theorem(implies(or(q, r), or(r, q))), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true), true)
% 0.18/0.48 = { by axiom 5 (axiom_1_6) }
% 0.18/0.48 ifeq(ifeq(true, true, theorem(implies(implies(or(q, r), or(r, q)), implies(or(p, or(q, r)), or(p, or(r, q))))), true), true, ifeq(theorem(implies(or(q, r), or(r, q))), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true), true)
% 0.18/0.48 = { by axiom 1 (ifeq_axiom) }
% 0.18/0.48 ifeq(theorem(implies(implies(or(q, r), or(r, q)), implies(or(p, or(q, r)), or(p, or(r, q))))), true, ifeq(theorem(implies(or(q, r), or(r, q))), true, theorem(implies(or(p, or(q, r)), or(p, or(r, q)))), true), true)
% 0.18/0.48 = { by axiom 4 (rule_2) }
% 0.18/0.48 true
% 0.18/0.48 % SZS output end Proof
% 0.18/0.48
% 0.18/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
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