%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SYN312-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 213.19s 27.08s
% Output : Proof 213.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN312-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n001.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 15:46:48 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 213.19/27.08 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
% 213.19/27.08
% 213.19/27.08 % SZS status Unsatisfiable
% 213.19/27.08
% 213.19/27.10 % SZS output start Proof
% 213.19/27.10 Axiom 1 (clause6): p(a, f(b), c) = true.
% 213.19/27.10 Axiom 2 (clause7): p(f(b), d, c) = true.
% 213.19/27.10 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 213.19/27.10 Axiom 4 (clause3): ifeq(p(X, Y, Z), true, p(Y, X, Z), true) = true.
% 213.19/27.10 Axiom 5 (clause2): ifeq(p(X, Y, Z), true, p(Z, Y, X), true) = true.
% 213.19/27.10 Axiom 6 (clause5): ifeq(p(X, Y, Z), true, p(g(X), Y, Z), true) = true.
% 213.19/27.10 Axiom 7 (clause4): ifeq(p(X, Y, Z), true, p(X, Y, f(Z)), true) = true.
% 213.19/27.10 Axiom 8 (clause1): ifeq(p(X, Y, Z), true, ifeq(p(W, X, Z), true, p(W, Y, Z), true), true) = true.
% 213.19/27.10
% 213.19/27.10 Goal 1 (clause8): p(f(g(a)), f(g(d)), f(g(c))) = true.
% 213.19/27.10 Proof:
% 213.19/27.10 p(f(g(a)), f(g(d)), f(g(c)))
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(true, true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 7 (clause4) R->L }
% 213.19/27.10 ifeq(ifeq(p(f(g(a)), f(b), g(c)), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(true, true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 7 (clause4) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(p(g(c), f(b), g(a)), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(c), f(b), g(a)), true), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 5 (clause2) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(g(a), f(b), c), true, p(c, f(b), g(a)), true), true, p(g(c), f(b), g(a)), true), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(a), f(b), c), true), true, p(c, f(b), g(a)), true), true, p(g(c), f(b), g(a)), true), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 1 (clause6) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(a, f(b), c), true, p(g(a), f(b), c), true), true, p(c, f(b), g(a)), true), true, p(g(c), f(b), g(a)), true), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 6 (clause5) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(c, f(b), g(a)), true), true, p(g(c), f(b), g(a)), true), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(p(c, f(b), g(a)), true, p(g(c), f(b), g(a)), true), true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 6 (clause5) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(true, true, p(g(c), f(b), f(g(a))), true), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(ifeq(ifeq(p(g(c), f(b), f(g(a))), true, p(f(g(a)), f(b), g(c)), true), true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 5 (clause2) }
% 213.19/27.10 ifeq(ifeq(true, true, p(f(g(a)), f(b), f(g(c))), true), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(true, true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 7 (clause4) R->L }
% 213.19/27.10 ifeq(ifeq(p(f(b), f(g(d)), g(c)), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(true, true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 5 (clause2) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(p(g(c), f(b), f(g(d))), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 6 (clause5) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(c, f(b), g(d)), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(c, f(b), g(d)), true), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 6 (clause5) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(d, f(b), c), true, p(g(d), f(b), c), true), true, p(c, f(b), g(d)), true), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(d, f(b), c), true), true, p(g(d), f(b), c), true), true, p(c, f(b), g(d)), true), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 2 (clause7) R->L }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(f(b), d, c), true, p(d, f(b), c), true), true, p(g(d), f(b), c), true), true, p(c, f(b), g(d)), true), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 4 (clause3) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(d), f(b), c), true), true, p(c, f(b), g(d)), true), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(p(g(d), f(b), c), true, p(c, f(b), g(d)), true), true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 5 (clause2) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, p(g(c), f(b), g(d)), true), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(ifeq(p(g(c), f(b), g(d)), true, p(g(c), f(b), f(g(d))), true), true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 7 (clause4) }
% 213.19/27.10 ifeq(ifeq(ifeq(ifeq(true, true, p(f(g(d)), f(b), g(c)), true), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(ifeq(ifeq(p(f(g(d)), f(b), g(c)), true, p(f(b), f(g(d)), g(c)), true), true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 4 (clause3) }
% 213.19/27.10 ifeq(ifeq(true, true, p(f(b), f(g(d)), f(g(c))), true), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 3 (ifeq_axiom) }
% 213.19/27.10 ifeq(p(f(b), f(g(d)), f(g(c))), true, ifeq(p(f(g(a)), f(b), f(g(c))), true, p(f(g(a)), f(g(d)), f(g(c))), true), true)
% 213.19/27.10 = { by axiom 8 (clause1) }
% 213.19/27.10 true
% 213.19/27.10 % SZS output end Proof
% 213.19/27.10
% 213.19/27.10 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------