%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 09:35:20 AM UTC 2026
% Result : Unsatisfiable 0.20s 0.40s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 3 RR)
% Number of literals : 60 ( 59 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 133 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
sum(x,x,x) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_equalities) ).
cnf(c2,axiom,
ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c3,plain,
ifeq2(true,true,ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),X3) = ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3) = ifeq2(true,true,ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
product(X2,multiplicative_identity,X2) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
true = product(X2,multiplicative_identity,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
ifeq2(true,true,ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),X3) = ifeq2(product(X3,multiplicative_identity,X3),true,ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),X3),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(c9,plain,
ifeq2(product(X3,multiplicative_identity,X3),true,ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
ifeq2(true,true,ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3),X3) = X3,
inference(transitivity,[status(thm)],[c7,c9]) ).
cnf(c11,plain,
ifeq2(product(X3,multiplicative_identity,X2),true,X2,X3) = X3,
inference(transitivity,[status(thm)],[c4,c10]) ).
cnf(c12,plain,
ifeq2(product(add(X2,X2),multiplicative_identity,X2),true,X2,add(X2,X2)) = add(X2,X2),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
add(X2,X2) = ifeq2(product(add(X2,X2),multiplicative_identity,X2),true,X2,add(X2,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
ifeq(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c15,plain,
ifeq(true,true,product(add(X2,X2),multiplicative_identity,X2),true) = product(add(X2,X2),multiplicative_identity,X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
product(add(X2,X2),multiplicative_identity,X2) = ifeq(true,true,product(add(X2,X2),multiplicative_identity,X2),true),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
sum(X2,Y2,add(X2,Y2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(c18,plain,
sum(X2,X2,add(X2,X2)) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
true = sum(X2,X2,add(X2,X2)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(true,true,product(add(X2,X2),multiplicative_identity,X2),true) = ifeq(sum(X2,X2,add(X2,X2)),true,product(add(X2,X2),multiplicative_identity,X2),true),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),true) = ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),
inference(substitution,[status(thm)],[c14]) ).
cnf(c22,plain,
ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true) = ifeq(true,true,ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),true),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
sum(inverse(X2),X2,multiplicative_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c24,plain,
true = sum(inverse(X2),X2,multiplicative_identity),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
ifeq(true,true,ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),true) = ifeq(sum(inverse(X3),X3,multiplicative_identity),true,ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),true),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
ifeq(true,true,ifeq(sum(inverse(X3),X2,X5),true,ifeq(sum(X3,X2,X4),true,product(X4,X5,X2),true),true),true) = ifeq(sum(inverse(X3),X2,X5),true,ifeq(sum(X3,X2,X4),true,product(X4,X5,X2),true),true),
inference(substitution,[status(thm)],[c14]) ).
cnf(c27,plain,
ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true) = ifeq(true,true,ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true),true),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
product(X2,inverse(X2),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c29,plain,
true = product(X2,inverse(X2),additive_identity),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(true,true,ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true),true) = ifeq(product(X5,inverse(X5),additive_identity),true,ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true),true),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(true,true,ifeq(sum(X4,X3,X2),true,ifeq(sum(X5,X3,X6),true,product(X6,X2,X3),true),true),true) = ifeq(sum(X4,X3,X2),true,ifeq(sum(X5,X3,X6),true,product(X6,X2,X3),true),true),
inference(substitution,[status(thm)],[c14]) ).
cnf(c32,plain,
ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true) = ifeq(true,true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true) = ifeq(product(X6,X5,additive_identity),true,ifeq(true,true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),true),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
sum(additive_identity,X2,X2) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c35,plain,
true = sum(additive_identity,X2,X2),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
ifeq(true,true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true) = ifeq(sum(additive_identity,X4,X4),true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(true,true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),true) = ifeq(product(X6,X5,additive_identity),true,ifeq(sum(additive_identity,X4,X4),true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),true),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,axiom,
ifeq(product(Y2,Z,V3),true,ifeq(sum(V3,X2,V4),true,ifeq(sum(Z,X2,V2),true,ifeq(sum(Y2,X2,V1),true,product(V1,V2,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity7) ).
cnf(c39,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(sum(additive_identity,X4,X4),true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),true) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(true,true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true),true) = true,
inference(transitivity,[status(thm)],[c37,c39]) ).
cnf(c41,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(sum(X5,X4,X3),true,ifeq(sum(X6,X4,X2),true,product(X2,X3,X4),true),true),true) = true,
inference(transitivity,[status(thm)],[c33,c40]) ).
cnf(c42,plain,
ifeq(product(X5,inverse(X5),additive_identity),true,ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq(true,true,ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true),true) = true,
inference(transitivity,[status(thm)],[c30,c42]) ).
cnf(c44,plain,
ifeq(sum(inverse(X5),X4,X3),true,ifeq(sum(X5,X4,X2),true,product(X2,X3,X4),true),true) = true,
inference(transitivity,[status(thm)],[c27,c43]) ).
cnf(c45,plain,
ifeq(sum(inverse(X3),X3,multiplicative_identity),true,ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),true) = true,
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(true,true,ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true),true) = true,
inference(transitivity,[status(thm)],[c25,c45]) ).
cnf(c47,plain,
ifeq(sum(X3,X3,X2),true,product(X2,multiplicative_identity,X3),true) = true,
inference(transitivity,[status(thm)],[c22,c46]) ).
cnf(c48,plain,
ifeq(sum(X2,X2,add(X2,X2)),true,product(add(X2,X2),multiplicative_identity,X2),true) = true,
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq(true,true,product(add(X2,X2),multiplicative_identity,X2),true) = true,
inference(transitivity,[status(thm)],[c20,c48]) ).
cnf(c50,plain,
product(add(X2,X2),multiplicative_identity,X2) = true,
inference(transitivity,[status(thm)],[c16,c49]) ).
cnf(c51,plain,
ifeq2(product(add(X2,X2),multiplicative_identity,X2),true,X2,add(X2,X2)) = ifeq2(true,true,X2,add(X2,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq2(true,true,X2,add(X2,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
ifeq2(product(add(X2,X2),multiplicative_identity,X2),true,X2,add(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c51,c52]) ).
cnf(c54,plain,
add(X2,X2) = X2,
inference(transitivity,[status(thm)],[c13,c53]) ).
cnf(c55,plain,
X2 = add(X2,X2),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
sum(X2,X2,X2) = sum(X2,X2,add(X2,X2)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
sum(X2,X2,add(X2,X2)) = true,
inference(substitution,[status(thm)],[c17]) ).
cnf(c58,plain,
sum(X2,X2,X2) = true,
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
sum(x,x,x) = true,
inference(substitution,[status(thm)],[c58]) ).
cnf(c60,plain,
$false,
inference(resolution,[status(thm)],[c1,c59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n008.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:03:54 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.40 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
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 1.23/0.40 % SZS output start CNFRefutation
% See solution above
% 1.23/0.44
% 1.23/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------