%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO017-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 09:35:26 AM UTC 2026
% Result : Unsatisfiable 27.33s 3.71s
% Output : CNFRefutation 28.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 14
% Syntax : Number of clauses : 207 ( 207 unt; 0 nHn; 38 RR)
% Number of literals : 207 ( 206 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 : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 469 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(x,z,x) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c3,plain,
ifeq(true,true,product(x,z,x),true) = product(x,z,x),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
product(x,z,x) = ifeq(true,true,product(x,z,x),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(c6,plain,
sum(x,additive_identity,x) = true,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
true = sum(x,additive_identity,x),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
ifeq(true,true,product(x,z,x),true) = ifeq(sum(x,additive_identity,x),true,product(x,z,x),true),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c10,plain,
ifeq2(true,true,multiply(x,z),x) = multiply(x,z),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(x,z) = ifeq2(true,true,multiply(x,z),x),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
ifeq(true,true,sum(additive_identity,x,multiply(x,z)),true) = sum(additive_identity,x,multiply(x,z)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c13,plain,
sum(additive_identity,x,multiply(x,z)) = ifeq(true,true,sum(additive_identity,x,multiply(x,z)),true),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
product(X2,Y,multiply(X2,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(c15,plain,
product(x,z,multiply(x,z)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
true = product(x,z,multiply(x,z)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
ifeq(true,true,sum(additive_identity,x,multiply(x,z)),true) = ifeq(product(x,z,multiply(x,z)),true,sum(additive_identity,x,multiply(x,z)),true),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,sum(additive_identity,x,X2),true) = sum(additive_identity,x,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
sum(additive_identity,x,X2) = ifeq(true,true,sum(additive_identity,x,X2),true),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
ifeq(product(x,z,X2),true,sum(additive_identity,x,X2),true) = ifeq(product(x,z,X2),true,ifeq(true,true,sum(additive_identity,x,X2),true),true),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
ifeq(true,true,sum(y,x,z),true) = sum(y,x,z),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
sum(y,x,z) = ifeq(true,true,sum(y,x,z),true),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
sum(x,y,z) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c24,plain,
true = sum(x,y,z),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
ifeq(true,true,sum(y,x,z),true) = ifeq(sum(x,y,z),true,sum(y,x,z),true),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
ifeq(sum(X2,Y2,Z),true,sum(Y2,X2,Z),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(c27,plain,
ifeq(sum(x,y,z),true,sum(y,x,z),true) = true,
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,sum(y,x,z),true) = true,
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
sum(y,x,z) = true,
inference(transitivity,[status(thm)],[c22,c28]) ).
cnf(c30,plain,
true = sum(y,x,z),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
ifeq(true,true,sum(additive_identity,x,X2),true) = ifeq(sum(y,x,z),true,sum(additive_identity,x,X2),true),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
ifeq(product(x,z,X2),true,ifeq(true,true,sum(additive_identity,x,X2),true),true) = ifeq(product(x,z,X2),true,ifeq(sum(y,x,z),true,sum(additive_identity,x,X2),true),true),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq2(true,true,multiply(X2,X4),X3) = multiply(X2,X4),
inference(substitution,[status(thm)],[c9]) ).
cnf(c34,plain,
multiply(X4,X3) = ifeq2(true,true,multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
ifeq2(product(X4,X3,X2),true,multiply(X4,X3),X2) = ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c34]) ).
cnf(c36,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c37,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c38,plain,
ifeq2(true,true,multiply(X4,X3),X2) = ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2) = ifeq2(product(X4,X3,X2),true,ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c38]) ).
cnf(c40,axiom,
ifeq2(product(X2,Y2,V),true,ifeq2(product(X2,Y2,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(c41,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),X2) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2) = X2,
inference(transitivity,[status(thm)],[c39,c41]) ).
cnf(c43,plain,
ifeq2(product(X4,X3,X2),true,multiply(X4,X3),X2) = X2,
inference(transitivity,[status(thm)],[c35,c42]) ).
cnf(c44,plain,
ifeq2(product(X2,X3,multiply(X3,X2)),true,multiply(X2,X3),multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(X3,X2) = ifeq2(product(X2,X3,multiply(X3,X2)),true,multiply(X2,X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq(true,true,product(X3,X2,multiply(X2,X3)),true) = product(X3,X2,multiply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
product(X3,X2,multiply(X2,X3)) = ifeq(true,true,product(X3,X2,multiply(X2,X3)),true),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
product(X2,X3,multiply(X2,X3)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c49,plain,
true = product(X2,X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
ifeq(true,true,product(X3,X2,multiply(X2,X3)),true) = ifeq(product(X2,X3,multiply(X2,X3)),true,product(X3,X2,multiply(X2,X3)),true),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,axiom,
ifeq(product(X2,Y2,Z2),true,product(Y2,X2,Z2),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
cnf(c52,plain,
ifeq(product(X2,X3,multiply(X2,X3)),true,product(X3,X2,multiply(X2,X3)),true) = true,
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq(true,true,product(X3,X2,multiply(X2,X3)),true) = true,
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
product(X3,X2,multiply(X2,X3)) = true,
inference(transitivity,[status(thm)],[c47,c53]) ).
cnf(c55,plain,
product(X2,X3,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
ifeq2(product(X2,X3,multiply(X3,X2)),true,multiply(X2,X3),multiply(X3,X2)) = ifeq2(true,true,multiply(X2,X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c57,plain,
ifeq2(true,true,multiply(X2,X3),multiply(X3,X2)) = multiply(X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c58,plain,
ifeq2(product(X2,X3,multiply(X3,X2)),true,multiply(X2,X3),multiply(X3,X2)) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
multiply(X3,X2) = multiply(X2,X3),
inference(transitivity,[status(thm)],[c45,c58]) ).
cnf(c60,plain,
multiply(X2,additive_identity) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
ifeq2(true,true,additive_identity,X2) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c63,plain,
additive_identity = ifeq2(true,true,additive_identity,X2),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
ifeq2(product(X3,inverse(X3),X2),true,additive_identity,X2) = ifeq2(product(X3,inverse(X3),X2),true,ifeq2(true,true,additive_identity,X2),X2),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,axiom,
product(X2,inverse(X2),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c66,plain,
true = product(X2,inverse(X2),additive_identity),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq2(true,true,additive_identity,X2) = ifeq2(product(X3,inverse(X3),additive_identity),true,additive_identity,X2),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
ifeq2(product(X3,inverse(X3),X2),true,ifeq2(true,true,additive_identity,X2),X2) = ifeq2(product(X3,inverse(X3),X2),true,ifeq2(product(X3,inverse(X3),additive_identity),true,additive_identity,X2),X2),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
ifeq2(product(X3,inverse(X3),X2),true,ifeq2(product(X3,inverse(X3),additive_identity),true,additive_identity,X2),X2) = X2,
inference(substitution,[status(thm)],[c40]) ).
cnf(c70,plain,
ifeq2(product(X3,inverse(X3),X2),true,ifeq2(true,true,additive_identity,X2),X2) = X2,
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
ifeq2(product(X3,inverse(X3),X2),true,additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c64,c70]) ).
cnf(c72,plain,
ifeq2(product(X2,inverse(X2),multiply(X2,additive_identity)),true,additive_identity,multiply(X2,additive_identity)) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
multiply(X2,additive_identity) = ifeq2(product(X2,inverse(X2),multiply(X2,additive_identity)),true,additive_identity,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,plain,
ifeq(true,true,product(X2,inverse(X2),multiply(X2,additive_identity)),true) = product(X2,inverse(X2),multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c75,plain,
product(X2,inverse(X2),multiply(X2,additive_identity)) = ifeq(true,true,product(X2,inverse(X2),multiply(X2,additive_identity)),true),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
product(X2,additive_identity,multiply(X2,additive_identity)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c77,plain,
true = product(X2,additive_identity,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c76]) ).
cnf(c78,plain,
ifeq(true,true,product(X2,inverse(X2),multiply(X2,additive_identity)),true) = ifeq(product(X2,additive_identity,multiply(X2,additive_identity)),true,product(X2,inverse(X2),multiply(X2,additive_identity)),true),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
ifeq(true,true,ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),true) = ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c80,plain,
ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true) = ifeq(true,true,ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),true),
inference(symmetry,[status(thm)],[c79]) ).
cnf(c81,plain,
true = product(X2,inverse(X2),additive_identity),
inference(symmetry,[status(thm)],[c65]) ).
cnf(c82,plain,
ifeq(true,true,ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),true) = ifeq(product(X3,inverse(X3),additive_identity),true,ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),true),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
ifeq(true,true,product(X4,X3,X2),true) = product(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c84,plain,
product(X4,X3,X2) = ifeq(true,true,product(X4,X3,X2),true),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
ifeq(product(X4,additive_identity,X2),true,product(X4,X3,X2),true) = ifeq(product(X4,additive_identity,X2),true,ifeq(true,true,product(X4,X3,X2),true),true),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,product(X4,X3,X2),true),true) = ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,ifeq(true,true,product(X4,X3,X2),true),true),true),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,axiom,
sum(additive_identity,X2,X2) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c88,plain,
true = sum(additive_identity,X2,X2),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
ifeq(true,true,product(X4,X3,X2),true) = ifeq(sum(additive_identity,X3,X3),true,product(X4,X3,X2),true),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
ifeq(product(X4,additive_identity,X2),true,ifeq(true,true,product(X4,X3,X2),true),true) = ifeq(product(X4,additive_identity,X2),true,ifeq(sum(additive_identity,X3,X3),true,product(X4,X3,X2),true),true),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,ifeq(true,true,product(X4,X3,X2),true),true),true) = ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,ifeq(sum(additive_identity,X3,X3),true,product(X4,X3,X2),true),true),true),
inference(congruence,[status(thm)],[c90]) ).
cnf(c92,plain,
ifeq(true,true,ifeq(sum(X2,X3,X5),true,product(X4,X5,X6),true),true) = ifeq(sum(X2,X3,X5),true,product(X4,X5,X6),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c93,plain,
ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true) = ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
ifeq(product(X6,X4,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true) = ifeq(product(X6,X4,X3),true,ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true) = ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),true),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
true = sum(X2,additive_identity,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c97,plain,
ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true) = ifeq(sum(X3,additive_identity,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
ifeq(product(X6,X4,X3),true,ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true) = ifeq(product(X6,X4,X3),true,ifeq(sum(X3,additive_identity,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),true) = ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,additive_identity,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),true),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,axiom,
ifeq(product(X2,Z2,V2),true,ifeq(product(X2,Y2,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y2,Z2,V3),true,product(X2,V3,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c101,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,additive_identity,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),true) = true,
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(true,true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true),true) = true,
inference(transitivity,[status(thm)],[c99,c101]) ).
cnf(c103,plain,
ifeq(product(X6,X5,additive_identity),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X4,X5,X2),true,product(X6,X2,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c95,c102]) ).
cnf(c104,plain,
ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,ifeq(sum(additive_identity,X3,X3),true,product(X4,X3,X2),true),true),true) = true,
inference(substitution,[status(thm)],[c103]) ).
cnf(c105,plain,
ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,ifeq(true,true,product(X4,X3,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c91,c104]) ).
cnf(c106,plain,
ifeq(product(X4,X3,additive_identity),true,ifeq(product(X4,additive_identity,X2),true,product(X4,X3,X2),true),true) = true,
inference(transitivity,[status(thm)],[c86,c105]) ).
cnf(c107,plain,
ifeq(product(X3,inverse(X3),additive_identity),true,ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),true) = true,
inference(substitution,[status(thm)],[c106]) ).
cnf(c108,plain,
ifeq(true,true,ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true),true) = true,
inference(transitivity,[status(thm)],[c82,c107]) ).
cnf(c109,plain,
ifeq(product(X3,additive_identity,X2),true,product(X3,inverse(X3),X2),true) = true,
inference(transitivity,[status(thm)],[c80,c108]) ).
cnf(c110,plain,
ifeq(product(X2,additive_identity,multiply(X2,additive_identity)),true,product(X2,inverse(X2),multiply(X2,additive_identity)),true) = true,
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
ifeq(true,true,product(X2,inverse(X2),multiply(X2,additive_identity)),true) = true,
inference(transitivity,[status(thm)],[c78,c110]) ).
cnf(c112,plain,
product(X2,inverse(X2),multiply(X2,additive_identity)) = true,
inference(transitivity,[status(thm)],[c75,c111]) ).
cnf(c113,plain,
ifeq2(product(X2,inverse(X2),multiply(X2,additive_identity)),true,additive_identity,multiply(X2,additive_identity)) = ifeq2(true,true,additive_identity,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c112]) ).
cnf(c114,plain,
ifeq2(true,true,additive_identity,multiply(X2,additive_identity)) = additive_identity,
inference(substitution,[status(thm)],[c9]) ).
cnf(c115,plain,
ifeq2(product(X2,inverse(X2),multiply(X2,additive_identity)),true,additive_identity,multiply(X2,additive_identity)) = additive_identity,
inference(transitivity,[status(thm)],[c113,c114]) ).
cnf(c116,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c73,c115]) ).
cnf(c117,plain,
multiply(additive_identity,X2) = additive_identity,
inference(transitivity,[status(thm)],[c61,c116]) ).
cnf(c118,plain,
additive_identity = multiply(additive_identity,X2),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
sum(additive_identity,X4,X3) = sum(multiply(additive_identity,X2),X4,X3),
inference(congruence,[status(thm)],[c118]) ).
cnf(c120,plain,
ifeq(sum(X2,X5,X4),true,sum(additive_identity,X5,X3),true) = ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X2,X5,X4),true,sum(additive_identity,X5,X3),true),true) = ifeq(product(X5,X4,X3),true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
ifeq(true,true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true) = ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c123,plain,
ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true) = ifeq(true,true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),
inference(symmetry,[status(thm)],[c122]) ).
cnf(c124,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true) = ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),true),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
product(additive_identity,X2,multiply(additive_identity,X2)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c126,plain,
true = product(additive_identity,X2,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
ifeq(true,true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true) = ifeq(product(additive_identity,X2,multiply(additive_identity,X2)),true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(additive_identity,X2,multiply(additive_identity,X2)),true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),true),
inference(congruence,[status(thm)],[c127]) ).
cnf(c129,plain,
ifeq(true,true,sum(X2,X4,X3),true) = sum(X2,X4,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c130,plain,
sum(X2,X4,X3) = ifeq(true,true,sum(X2,X4,X3),true),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
ifeq(sum(X3,X6,X5),true,sum(X2,X6,X4),true) = ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,sum(X2,X6,X4),true),true) = ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true),true),
inference(congruence,[status(thm)],[c131]) ).
cnf(c133,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,sum(X2,X6,X4),true),true),true) = ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true),true),true),
inference(congruence,[status(thm)],[c132]) ).
cnf(c134,plain,
true = sum(additive_identity,X2,X2),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c135,plain,
ifeq(true,true,sum(X2,X4,X3),true) = ifeq(sum(additive_identity,X4,X4),true,sum(X2,X4,X3),true),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true) = ifeq(sum(X3,X6,X5),true,ifeq(sum(additive_identity,X6,X6),true,sum(X2,X6,X4),true),true),
inference(congruence,[status(thm)],[c135]) ).
cnf(c137,plain,
ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true),true) = ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(sum(additive_identity,X6,X6),true,sum(X2,X6,X4),true),true),true),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true),true),true) = ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(sum(additive_identity,X6,X6),true,sum(X2,X6,X4),true),true),true),true),
inference(congruence,[status(thm)],[c137]) ).
cnf(c139,axiom,
ifeq(product(V1_2,V2_2,V4_2),true,ifeq(product(Y2,Z2,V3_2),true,ifeq(sum(Z2,X2,V2_2),true,ifeq(sum(Y2,X2,V1_2),true,sum(V3_2,X2,V4_2),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
cnf(c140,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(sum(additive_identity,X6,X6),true,sum(X2,X6,X4),true),true),true),true) = true,
inference(substitution,[status(thm)],[c139]) ).
cnf(c141,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,ifeq(true,true,sum(X2,X6,X4),true),true),true),true) = true,
inference(transitivity,[status(thm)],[c138,c140]) ).
cnf(c142,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(additive_identity,X3,X2),true,ifeq(sum(X3,X6,X5),true,sum(X2,X6,X4),true),true),true) = true,
inference(transitivity,[status(thm)],[c133,c141]) ).
cnf(c143,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(additive_identity,X2,multiply(additive_identity,X2)),true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c128,c143]) ).
cnf(c145,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X2,X5,X4),true,sum(multiply(additive_identity,X2),X5,X3),true),true) = true,
inference(transitivity,[status(thm)],[c124,c144]) ).
cnf(c146,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X2,X5,X4),true,sum(additive_identity,X5,X3),true),true) = true,
inference(transitivity,[status(thm)],[c121,c145]) ).
cnf(c147,plain,
ifeq(product(x,z,X2),true,ifeq(sum(y,x,z),true,sum(additive_identity,x,X2),true),true) = true,
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
ifeq(product(x,z,X2),true,ifeq(true,true,sum(additive_identity,x,X2),true),true) = true,
inference(transitivity,[status(thm)],[c32,c147]) ).
cnf(c149,plain,
ifeq(product(x,z,X2),true,sum(additive_identity,x,X2),true) = true,
inference(transitivity,[status(thm)],[c20,c148]) ).
cnf(c150,plain,
ifeq(product(x,z,multiply(x,z)),true,sum(additive_identity,x,multiply(x,z)),true) = true,
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
ifeq(true,true,sum(additive_identity,x,multiply(x,z)),true) = true,
inference(transitivity,[status(thm)],[c17,c150]) ).
cnf(c152,plain,
sum(additive_identity,x,multiply(x,z)) = true,
inference(transitivity,[status(thm)],[c13,c151]) ).
cnf(c153,plain,
true = sum(additive_identity,x,multiply(x,z)),
inference(symmetry,[status(thm)],[c152]) ).
cnf(c154,plain,
ifeq2(true,true,multiply(x,z),x) = ifeq2(sum(additive_identity,x,multiply(x,z)),true,multiply(x,z),x),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
ifeq2(true,true,ifeq2(sum(additive_identity,X3,X2),true,X2,X3),X3) = ifeq2(sum(additive_identity,X3,X2),true,X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c156,plain,
ifeq2(sum(additive_identity,X3,X2),true,X2,X3) = ifeq2(true,true,ifeq2(sum(additive_identity,X3,X2),true,X2,X3),X3),
inference(symmetry,[status(thm)],[c155]) ).
cnf(c157,plain,
true = sum(additive_identity,X2,X2),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c158,plain,
ifeq2(true,true,ifeq2(sum(additive_identity,X3,X2),true,X2,X3),X3) = ifeq2(sum(additive_identity,X3,X3),true,ifeq2(sum(additive_identity,X3,X2),true,X2,X3),X3),
inference(congruence,[status(thm)],[c157]) ).
cnf(c159,axiom,
ifeq2(sum(X2,Y2,V5),true,ifeq2(sum(X2,Y2,U2),true,U2,V5),V5) = V5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(c160,plain,
ifeq2(sum(additive_identity,X3,X3),true,ifeq2(sum(additive_identity,X3,X2),true,X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
ifeq2(true,true,ifeq2(sum(additive_identity,X3,X2),true,X2,X3),X3) = X3,
inference(transitivity,[status(thm)],[c158,c160]) ).
cnf(c162,plain,
ifeq2(sum(additive_identity,X3,X2),true,X2,X3) = X3,
inference(transitivity,[status(thm)],[c156,c161]) ).
cnf(c163,plain,
ifeq2(sum(additive_identity,x,multiply(x,z)),true,multiply(x,z),x) = x,
inference(substitution,[status(thm)],[c162]) ).
cnf(c164,plain,
ifeq2(true,true,multiply(x,z),x) = x,
inference(transitivity,[status(thm)],[c154,c163]) ).
cnf(c165,plain,
multiply(x,z) = x,
inference(transitivity,[status(thm)],[c11,c164]) ).
cnf(c166,plain,
x = multiply(x,z),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
sum(x,additive_identity,x) = sum(multiply(x,z),additive_identity,x),
inference(congruence,[status(thm)],[c166]) ).
cnf(c168,plain,
ifeq(sum(x,additive_identity,x),true,product(x,z,x),true) = ifeq(sum(multiply(x,z),additive_identity,x),true,product(x,z,x),true),
inference(congruence,[status(thm)],[c167]) ).
cnf(c169,plain,
ifeq(true,true,ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),true) = ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c170,plain,
ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true) = ifeq(true,true,ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),true),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c172,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c171]) ).
cnf(c173,plain,
ifeq(true,true,ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),true) = ifeq(product(X4,X3,multiply(X4,X3)),true,ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),true),
inference(congruence,[status(thm)],[c172]) ).
cnf(c174,plain,
additive_identity = multiply(X2,additive_identity),
inference(symmetry,[status(thm)],[c116]) ).
cnf(c175,plain,
sum(X3,additive_identity,X2) = sum(X3,multiply(X4,additive_identity),X2),
inference(congruence,[status(thm)],[c174]) ).
cnf(c176,plain,
ifeq(sum(X3,additive_identity,X2),true,product(X5,X4,X2),true) = ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),
inference(congruence,[status(thm)],[c175]) ).
cnf(c177,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X3,additive_identity,X2),true,product(X5,X4,X2),true),true) = ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c179,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true) = ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),true),
inference(symmetry,[status(thm)],[c178]) ).
cnf(c180,plain,
product(X2,additive_identity,multiply(X2,additive_identity)) = true,
inference(substitution,[status(thm)],[c14]) ).
cnf(c181,plain,
true = product(X2,additive_identity,multiply(X2,additive_identity)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),true) = ifeq(product(X5,additive_identity,multiply(X5,additive_identity)),true,ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),true),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
ifeq(true,true,product(X4,X3,X2),true) = product(X4,X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c184,plain,
product(X4,X3,X2) = ifeq(true,true,product(X4,X3,X2),true),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,plain,
ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true) = ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),
inference(congruence,[status(thm)],[c184]) ).
cnf(c186,plain,
ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true),true) = ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),
inference(congruence,[status(thm)],[c185]) ).
cnf(c187,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true),true),true) = ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),true),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
true = sum(X2,additive_identity,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c189,plain,
ifeq(true,true,product(X4,X3,X2),true) = ifeq(sum(X3,additive_identity,X3),true,product(X4,X3,X2),true),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true) = ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),
inference(congruence,[status(thm)],[c189]) ).
cnf(c191,plain,
ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true) = ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),true),
inference(congruence,[status(thm)],[c190]) ).
cnf(c192,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),true) = ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),true),true),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(sum(X4,additive_identity,X4),true,product(X6,X4,X2),true),true),true),true) = true,
inference(substitution,[status(thm)],[c100]) ).
cnf(c194,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,ifeq(true,true,product(X6,X4,X2),true),true),true),true) = true,
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
ifeq(product(X6,additive_identity,X5),true,ifeq(product(X6,X4,X3),true,ifeq(sum(X3,X5,X2),true,product(X6,X4,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c187,c194]) ).
cnf(c196,plain,
ifeq(product(X5,additive_identity,multiply(X5,additive_identity)),true,ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),true) = true,
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true),true) = true,
inference(transitivity,[status(thm)],[c182,c196]) ).
cnf(c198,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X3,multiply(X5,additive_identity),X2),true,product(X5,X4,X2),true),true) = true,
inference(transitivity,[status(thm)],[c179,c197]) ).
cnf(c199,plain,
ifeq(product(X5,X4,X3),true,ifeq(sum(X3,additive_identity,X2),true,product(X5,X4,X2),true),true) = true,
inference(transitivity,[status(thm)],[c177,c198]) ).
cnf(c200,plain,
ifeq(product(X4,X3,multiply(X4,X3)),true,ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),true) = true,
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
ifeq(true,true,ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true),true) = true,
inference(transitivity,[status(thm)],[c173,c200]) ).
cnf(c202,plain,
ifeq(sum(multiply(X4,X3),additive_identity,X2),true,product(X4,X3,X2),true) = true,
inference(transitivity,[status(thm)],[c170,c201]) ).
cnf(c203,plain,
ifeq(sum(multiply(x,z),additive_identity,x),true,product(x,z,x),true) = true,
inference(substitution,[status(thm)],[c202]) ).
cnf(c204,plain,
ifeq(sum(x,additive_identity,x),true,product(x,z,x),true) = true,
inference(transitivity,[status(thm)],[c168,c203]) ).
cnf(c205,plain,
ifeq(true,true,product(x,z,x),true) = true,
inference(transitivity,[status(thm)],[c8,c204]) ).
cnf(c206,plain,
product(x,z,x) = true,
inference(transitivity,[status(thm)],[c4,c205]) ).
cnf(c207,plain,
$false,
inference(resolution,[status(thm)],[c1,c206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO017-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n013.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:03:36 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.33/3.71 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
% 27.33/3.71
% 27.33/3.71 % SZS status Unsatisfiable
% 27.33/3.71
% 27.33/3.72 % SZS output start CNFRefutation
% See solution above
% 28.12/3.85
% 28.12/3.85 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------