%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN310-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 01:47:31 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.29s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN310-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n016.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 15:45:48 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.29 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.11/0.29
% 0.11/0.29 % SZS status Unsatisfiable
% 0.11/0.29
% 0.23/0.32 % SZS output start Proof
% 0.23/0.32 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.23/0.32 Axiom 2 (clause6): p(f(g(a)), f(g(b)), f(g(c))) = true.
% 0.23/0.32 Axiom 3 (clause2): ifeq(p(X, Y, Z), true, p(Y, X, Z), true) = true.
% 0.23/0.32 Axiom 4 (clause1): ifeq(p(X, Y, Z), true, p(Z, Y, X), true) = true.
% 0.23/0.32 Axiom 5 (clause4): ifeq(p(f(X), Y, Z), true, p(X, Y, Z), true) = true.
% 0.23/0.32 Axiom 6 (clause3): ifeq(p(X, Y, g(Z)), true, p(X, Y, Z), true) = true.
% 0.23/0.32
% 0.23/0.32 Goal 1 (clause5): p(a, b, c) = true.
% 0.23/0.32 Proof:
% 0.23/0.32 p(a, b, c)
% 0.23/0.32 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.32 ifeq(true, true, p(a, b, c), true)
% 0.23/0.32 = { by axiom 6 (clause3) R->L }
% 0.23/0.32 ifeq(ifeq(p(c, b, g(a)), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.32 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.32 ifeq(ifeq(ifeq(true, true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 3 (clause2) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(p(b, g(a), c), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 4 (clause1) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(g(c), g(a), b), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 5 (clause4) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(f(g(c)), g(a), g(b)), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 5 (clause4) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(f(g(b)), g(a), f(g(c))), true, p(g(b), g(a), f(g(c))), true), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 1 (ifeq_axiom) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(f(g(b)), g(a), f(g(c))), true), true, p(g(b), g(a), f(g(c))), true), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 5 (clause4) R->L }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(f(g(a)), f(g(b)), f(g(c))), true, p(g(a), f(g(b)), f(g(c))), true), true, p(f(g(b)), g(a), f(g(c))), true), true, p(g(b), g(a), f(g(c))), true), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.33 = { by axiom 2 (clause6) }
% 0.23/0.33 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(a), f(g(b)), f(g(c))), true), true, p(f(g(b)), g(a), f(g(c))), true), true, p(g(b), g(a), f(g(c))), true), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(g(a), f(g(b)), f(g(c))), true, p(f(g(b)), g(a), f(g(c))), true), true, p(g(b), g(a), f(g(c))), true), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 3 (clause2) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(b), g(a), f(g(c))), true), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(g(b), g(a), f(g(c))), true, p(f(g(c)), g(a), g(b)), true), true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 4 (clause1) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(c), g(a), g(b)), true), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(g(c), g(a), g(b)), true, p(g(c), g(a), b), true), true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 6 (clause3) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(b, g(a), g(c)), true), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(ifeq(p(b, g(a), g(c)), true, p(b, g(a), c), true), true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 6 (clause3) }
% 0.23/0.34 ifeq(ifeq(ifeq(ifeq(true, true, p(g(a), b, c), true), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.23/0.34 ifeq(ifeq(ifeq(p(g(a), b, c), true, p(c, b, g(a)), true), true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 4 (clause1) }
% 0.23/0.34 ifeq(ifeq(true, true, p(c, b, a), true), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 1 (ifeq_axiom) }
% 0.23/0.34 ifeq(p(c, b, a), true, p(a, b, c), true)
% 0.23/0.34 = { by axiom 4 (clause1) }
% 0.23/0.34 true
% 0.23/0.34 % SZS output end Proof
% 0.23/0.34
% 0.23/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------