%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% 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 12:39:13 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.36s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : Mon Sep 28 02:57:19 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 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
% 0.07/0.36
% 0.07/0.36 % SZS status Unsatisfiable
% 0.07/0.36
% 0.07/0.36 % SZS output start Proof
% 0.07/0.36 Axiom 1 (cls_conjecture_0): v_f(v_g(v_x)) = v_x.
% 0.07/0.36 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.36 Axiom 3 (cls_conjecture_1): ifeq(v_f(v_g(X)), X, X, v_x) = v_x.
% 0.07/0.36 Axiom 4 (cls_conjecture_2): ifeq(v_g(v_f(X)), X, v_g(v_f(v_xa(X))), v_xa(X)) = v_xa(X).
% 0.07/0.36
% 0.07/0.36 Goal 1 (cls_conjecture_3): tuple(v_g(v_f(X)), v_xa(X)) = tuple(X, X).
% 0.07/0.36 The goal is true when:
% 0.07/0.36 X = v_g(v_x)
% 0.07/0.36
% 0.07/0.36 Proof:
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), v_xa(v_g(v_x)))
% 0.07/0.36 = { by axiom 4 (cls_conjecture_2) R->L }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(v_f(v_xa(v_g(v_x)))), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 2 (ifeq_axiom) R->L }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(ifeq(v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))), v_x)), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 4 (cls_conjecture_2) R->L }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(ifeq(v_f(ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(v_f(v_xa(v_g(v_x)))), v_xa(v_g(v_x)))), v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))), v_x)), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 1 (cls_conjecture_0) }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(ifeq(v_f(ifeq(v_g(v_x), v_g(v_x), v_g(v_f(v_xa(v_g(v_x)))), v_xa(v_g(v_x)))), v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))), v_x)), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(ifeq(v_f(v_g(v_f(v_xa(v_g(v_x))))), v_f(v_xa(v_g(v_x))), v_f(v_xa(v_g(v_x))), v_x)), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 3 (cls_conjecture_1) }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_f(v_g(v_x))), v_g(v_x), v_g(v_x), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 1 (cls_conjecture_0) }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), ifeq(v_g(v_x), v_g(v_x), v_g(v_x), v_xa(v_g(v_x))))
% 0.07/0.36 = { by axiom 2 (ifeq_axiom) }
% 0.07/0.36 tuple(v_g(v_f(v_g(v_x))), v_g(v_x))
% 0.07/0.36 = { by axiom 1 (cls_conjecture_0) }
% 0.07/0.36 tuple(v_g(v_x), v_g(v_x))
% 0.07/0.36 % SZS output end Proof
% 0.07/0.36
% 0.07/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------