%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG025-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 : Fri Sep 25 02:37:30 PM UTC 2026
% Result : Unsatisfiable 28.38s 4.10s
% Output : Proof 28.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 131 ( 131 unt; 0 def)
% Number of atoms : 131 ( 130 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 255 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_over_add1) ).
fof(f6_nnf,plain,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t16,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(f8,axiom,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_alternative) ).
fof(f8_nnf,plain,
! [X,Y] : multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] : multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
multiply(multiply(X0,X1),X1) = multiply(X0,multiply(X1,X1)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t15,plain,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t27,plain,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
inference(orient,[status(thm)],[t15]) ).
cnf(t33,plain,
multiply(multiply(X1,X2),add(X2,X3)) = add(multiply(X1,multiply(X2,X2)),multiply(multiply(X1,X2),X3)),
inference(cp,[status(thm)],[t32,t27]) ).
cnf(t3708,plain,
add(multiply(X1,multiply(X2,X2)),multiply(multiply(X1,X2),X3)) = multiply(multiply(X1,X2),add(X2,X3)),
inference(orient,[status(thm)],[t33]) ).
cnf(f7,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_over_add2) ).
fof(f7_nnf,plain,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t17,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t45,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t47,plain,
multiply(add(multiply(X1,X2),X3),X2) = add(multiply(X1,multiply(X2,X2)),multiply(X3,X2)),
inference(cp,[status(thm)],[t45,t27]) ).
cnf(f13,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f13_nnf,plain,
! [X,Y] : add(X,Y) = add(Y,X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] : add(X,Y) = add(Y,X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t6,plain,
add(X1,X2) = add(X2,X1),
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t66,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t58444,plain,
multiply(add(X3,multiply(X1,X2)),X2) = add(multiply(X1,multiply(X2,X2)),multiply(X3,X2)),
inference(step,[status(thm)],[t47,t66]) ).
cnf(t58445,plain,
multiply(add(X3,multiply(X1,X2)),X2) = add(multiply(X3,X2),multiply(X1,multiply(X2,X2))),
inference(step,[status(thm)],[t58444,t66]) ).
cnf(t4814,plain,
add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
inference(orient,[status(thm)],[t58445]) ).
cnf(f9,axiom,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_alternative) ).
fof(f9_nnf,plain,
! [X,Y] : multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] : multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
multiply(multiply(X0,X0),X1) = multiply(X0,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t14,plain,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t29,plain,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
inference(orient,[status(thm)],[t14]) ).
cnf(t4828,plain,
multiply(add(multiply(X1,X1),multiply(X2,X3)),X3) = add(multiply(X1,multiply(X1,X3)),multiply(X2,multiply(X3,X3))),
inference(cp,[status(thm)],[t4814,t29]) ).
cnf(t53943,plain,
add(multiply(X1,multiply(X1,X2)),multiply(X3,multiply(X2,X2))) = multiply(add(multiply(X1,X1),multiply(X3,X2)),X2),
inference(orient,[status(thm)],[t4828]) ).
cnf(t53945,plain,
multiply(add(multiply(X1,X1),multiply(X1,X2)),X2) = multiply(X1,add(multiply(X1,X2),multiply(X2,X2))),
inference(cp,[status(thm)],[t53943,t32]) ).
cnf(t59052,plain,
multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,add(multiply(X1,X2),multiply(X2,X2))),
inference(step,[status(thm)],[t53945,t32]) ).
cnf(t59053,plain,
multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,multiply(add(X1,X2),X2)),
inference(step,[status(thm)],[t59052,t45]) ).
cnf(t54565,plain,
multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,multiply(add(X1,X2),X2)),
inference(orient,[status(thm)],[t59053]) ).
cnf(f14,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f14_nnf,plain,
! [X,Y,Z] : add(X,add(Y,Z)) = add(add(X,Y),Z),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X,Y,Z] : add(X,add(Y,Z)) = add(add(X,Y),Z),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t11,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t58287,plain,
add(X3,add(X1,X2)) = add(X1,add(X2,X3)),
inference(step,[status(thm)],[t11,t66]) ).
cnf(t73,plain,
add(X1,add(X2,X3)) = add(X2,add(X3,X1)),
inference(orient,[status(thm)],[t58287]) ).
cnf(f3,axiom,
add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_inverse) ).
fof(f3_nnf,plain,
! [X] : add(additive_inverse(X),X) = additive_identity,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : add(additive_inverse(X),X) = additive_identity,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t5,plain,
add(additive_inverse(X1),X1) = additive_identity,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t58288,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t5,t66]) ).
cnf(t91,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t58288]) ).
cnf(t95,plain,
add(X1,add(additive_inverse(X1),X2)) = add(X2,additive_identity),
inference(cp,[status(thm)],[t73,t91]) ).
cnf(t58293,plain,
add(X1,add(X2,additive_inverse(X1))) = add(X2,additive_identity),
inference(step,[status(thm)],[t95,t66]) ).
cnf(f0,axiom,
add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f0_nnf,plain,
! [X] : add(additive_identity,X) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : add(additive_identity,X) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
add(additive_identity,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t18,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t71,plain,
add(additive_identity,X1) = X1,
inference(rw,[status(thm)],[t18]) ).
cnf(t58289,plain,
add(X1,additive_identity) = X1,
inference(step,[status(thm)],[t71,t66]) ).
cnf(t112,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t58289]) ).
cnf(t58294,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(step,[status(thm)],[t58293,t112]) ).
cnf(t136,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t58294]) ).
cnf(t54581,plain,
multiply(X1,multiply(add(X1,add(X2,additive_inverse(X1))),add(X2,additive_inverse(X1)))) = multiply(multiply(X1,X2),add(X2,additive_inverse(X1))),
inference(cp,[status(thm)],[t54565,t136]) ).
cnf(t59055,plain,
multiply(X1,multiply(X2,add(X2,additive_inverse(X1)))) = multiply(multiply(X1,X2),add(X2,additive_inverse(X1))),
inference(step,[status(thm)],[t54581,t136]) ).
cnf(t55147,plain,
multiply(multiply(X1,X2),add(X2,additive_inverse(X1))) = multiply(X1,multiply(X2,add(X2,additive_inverse(X1)))),
inference(orient,[status(thm)],[t59055]) ).
cnf(f10,axiom,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
fof(f10_nnf,plain,
! [X,Y] : multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] : multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t9,plain,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f11,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
fof(f11_nnf,plain,
! [X,Y] : multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] : multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t8,plain,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t39,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(orient,[status(thm)],[t8]) ).
cnf(t58286,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(step,[status(thm)],[t9,t39]) ).
cnf(t55,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(orient,[status(thm)],[t58286]) ).
cnf(t55176,plain,
multiply(additive_inverse(X1),multiply(X2,add(X2,additive_inverse(additive_inverse(X1))))) = multiply(multiply(X1,additive_inverse(X2)),add(X2,additive_inverse(additive_inverse(X1)))),
inference(cp,[status(thm)],[t55147,t55]) ).
cnf(t59105,plain,
multiply(X1,additive_inverse(multiply(X2,add(X2,additive_inverse(additive_inverse(X1)))))) = multiply(multiply(X1,additive_inverse(X2)),add(X2,additive_inverse(additive_inverse(X1)))),
inference(step,[status(thm)],[t55176,t55]) ).
cnf(t59106,plain,
multiply(X1,multiply(X2,additive_inverse(add(X2,additive_inverse(additive_inverse(X1)))))) = multiply(multiply(X1,additive_inverse(X2)),add(X2,additive_inverse(additive_inverse(X1)))),
inference(step,[status(thm)],[t59105,t39]) ).
cnf(f4,axiom,
additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_of_inverses) ).
fof(f4_nnf,plain,
! [X,Y] : additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t10,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t97,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(orient,[status(thm)],[t10]) ).
cnf(f5,axiom,
additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f5_nnf,plain,
! [X] : additive_inverse(additive_inverse(X)) = X,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : additive_inverse(additive_inverse(X)) = X,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t2,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t19,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t100,plain,
additive_inverse(add(additive_inverse(X1),X2)) = add(X1,additive_inverse(X2)),
inference(cp,[status(thm)],[t97,t19]) ).
cnf(t58292,plain,
additive_inverse(add(X2,additive_inverse(X1))) = add(X1,additive_inverse(X2)),
inference(step,[status(thm)],[t100,t66]) ).
cnf(t125,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(orient,[status(thm)],[t58292]) ).
cnf(t59107,plain,
multiply(X1,multiply(X2,add(additive_inverse(X1),additive_inverse(X2)))) = multiply(multiply(X1,additive_inverse(X2)),add(X2,additive_inverse(additive_inverse(X1)))),
inference(step,[status(thm)],[t59106,t125]) ).
cnf(t59108,plain,
multiply(X1,multiply(X2,additive_inverse(add(X1,X2)))) = multiply(multiply(X1,additive_inverse(X2)),add(X2,additive_inverse(additive_inverse(X1)))),
inference(step,[status(thm)],[t59107,t97]) ).
cnf(t57,plain,
multiply(multiply(X1,X2),additive_inverse(X3)) = multiply(multiply(X1,additive_inverse(X2)),X3),
inference(cp,[status(thm)],[t55,t39]) ).
cnf(t321,plain,
multiply(multiply(X1,additive_inverse(X2)),X3) = multiply(multiply(X1,X2),additive_inverse(X3)),
inference(orient,[status(thm)],[t57]) ).
cnf(t59109,plain,
multiply(X1,multiply(X2,additive_inverse(add(X1,X2)))) = multiply(multiply(X1,X2),additive_inverse(add(X2,additive_inverse(additive_inverse(X1))))),
inference(step,[status(thm)],[t59108,t321]) ).
cnf(t59110,plain,
multiply(X1,multiply(X2,additive_inverse(add(X1,X2)))) = multiply(multiply(X1,X2),add(additive_inverse(X1),additive_inverse(X2))),
inference(step,[status(thm)],[t59109,t125]) ).
cnf(t59111,plain,
multiply(X1,multiply(X2,additive_inverse(add(X1,X2)))) = multiply(multiply(X1,X2),additive_inverse(add(X1,X2))),
inference(step,[status(thm)],[t59110,t97]) ).
cnf(t57396,plain,
multiply(multiply(X1,X2),additive_inverse(add(X1,X2))) = multiply(X1,multiply(X2,additive_inverse(add(X1,X2)))),
inference(orient,[status(thm)],[t59111]) ).
cnf(t57625,plain,
multiply(multiply(X1,X2),add(X2,additive_inverse(add(X1,X2)))) = add(multiply(X1,multiply(X2,X2)),multiply(X1,multiply(X2,additive_inverse(add(X1,X2))))),
inference(cp,[status(thm)],[t3708,t57396]) ).
cnf(t138,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t136,t97]) ).
cnf(t148,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t138]) ).
cnf(t59112,plain,
multiply(multiply(X1,X2),additive_inverse(X1)) = add(multiply(X1,multiply(X2,X2)),multiply(X1,multiply(X2,additive_inverse(add(X1,X2))))),
inference(step,[status(thm)],[t57625,t148]) ).
cnf(t59113,plain,
multiply(multiply(X1,X2),additive_inverse(X1)) = multiply(X1,add(multiply(X2,X2),multiply(X2,additive_inverse(add(X1,X2))))),
inference(step,[status(thm)],[t59112,t32]) ).
cnf(t59114,plain,
multiply(multiply(X1,X2),additive_inverse(X1)) = multiply(X1,multiply(X2,add(X2,additive_inverse(add(X1,X2))))),
inference(step,[status(thm)],[t59113,t32]) ).
cnf(t59115,plain,
multiply(multiply(X1,X2),additive_inverse(X1)) = multiply(X1,multiply(X2,additive_inverse(X1))),
inference(step,[status(thm)],[t59114,t148]) ).
cnf(t57722,plain,
multiply(multiply(X1,X2),additive_inverse(X1)) = multiply(X1,multiply(X2,additive_inverse(X1))),
inference(orient,[status(thm)],[t59115]) ).
cnf(t57727,plain,
multiply(X1,multiply(additive_inverse(X2),additive_inverse(X1))) = multiply(multiply(X1,X2),additive_inverse(additive_inverse(X1))),
inference(cp,[status(thm)],[t57722,t321]) ).
cnf(t59116,plain,
multiply(X1,multiply(X2,additive_inverse(additive_inverse(X1)))) = multiply(multiply(X1,X2),additive_inverse(additive_inverse(X1))),
inference(step,[status(thm)],[t57727,t55]) ).
cnf(t59117,plain,
multiply(X1,multiply(X2,X1)) = multiply(multiply(X1,X2),additive_inverse(additive_inverse(X1))),
inference(step,[status(thm)],[t59116,t19]) ).
cnf(t59118,plain,
multiply(X1,multiply(X2,X1)) = multiply(multiply(X1,X2),X1),
inference(step,[status(thm)],[t59117,t19]) ).
cnf(t58031,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(orient,[status(thm)],[t59118]) ).
cnf(f17,negated_conjecture,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_middle_law) ).
fof(f17_nnf,plain,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
multiply(cy,multiply(cx,cy)) != multiply(cy,multiply(cx,cy)),
inference(rw,[status(thm)],[goal_0,t58031]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG025-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 07:49:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.38/4.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.38/4.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------