%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 02:37:22 PM UTC 2026
% Result : Unsatisfiable 36.07s 5.34s
% Output : Proof 36.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 16
% Syntax : Number of formulae : 189 ( 157 unt; 0 def)
% Number of atoms : 285 ( 136 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 198 ( 102 ~; 96 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 471 ( 24 sgn 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f12_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f2,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f2_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f1,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f1_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f3,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f3_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t143,plain,
product(X1,X2,add(multiply(X1,X2),multiply(X1,additive_identity))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2,hi2,hi1,hi3]) ).
cnf(f7,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f7_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X0,X4,X5),true,sum(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f0,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f0_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h23,plain,
sum(V0,V1,add(additive_identity,add(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,hi3,hi3]) ).
cnf(f11,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f11_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(product(X0,X5,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h16,plain,
sum(multiply(V0,V1),multiply(V0,V2),multiply(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi3,hi2]) ).
cnf(f15,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f15_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t228,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h16,h23]) ).
cnf(h28,plain,
sum(add(additive_identity,V0),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi1,hi0]) ).
cnf(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi3,hi3]) ).
cnf(t60,plain,
add(add(additive_identity,X1),add(additive_identity,additive_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi15,h21,h28]) ).
cnf(t13,plain,
add(X1,add(additive_identity,additive_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi1,h21]) ).
cnf(t256,plain,
add(X1,add(additive_identity,additive_identity)) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t4507,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t60,t256]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t4507]) ).
cnf(t4512,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t228,t258]) ).
cnf(t287,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t4512]) ).
cnf(t4521,plain,
product(X1,X2,multiply(X1,add(X2,additive_identity))) = true,
inference(step,[status(thm)],[t143,t287]) ).
cnf(t1,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi1,hi3]) ).
cnf(t257,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t4522,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(step,[status(thm)],[t4521,t257]) ).
cnf(t472,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t4522]) ).
cnf(f13,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f13_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(product(X5,X1,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h12,plain,
sum(multiply(V0,V1),multiply(V2,V1),multiply(add(V0,V2),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi3,hi2]) ).
cnf(t229,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi15,h12,h23]) ).
cnf(t4511,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t229,t258]) ).
cnf(t283,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t4511]) ).
cnf(f16,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f16_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t244,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t262,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t244]) ).
cnf(t477,plain,
X1 = ifeq(true,true,ifeq(product(X2,X3,X1),true,multiply(X2,X3),X1),X1),
inference(cp,[status(thm)],[t262,t472]) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t259,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t4559,plain,
X1 = ifeq(product(X2,X3,X1),true,multiply(X2,X3),X1),
inference(step,[status(thm)],[t477,t259]) ).
cnf(t3859,plain,
ifeq(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(orient,[status(thm)],[t4559]) ).
cnf(h3,plain,
sum(multiply(V0,V1),multiply(V0,additive_identity),multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi1,hi2]) ).
cnf(f14,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f14_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t91,plain,
product(add(X1,X1),additive_identity,multiply(X1,additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi3,h3]) ).
cnf(t493,plain,
product(add(X1,X1),additive_identity,multiply(X1,additive_identity)) = true,
inference(orient,[status(thm)],[t91]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(t168,plain,
add(add(X1,X2),add(additive_identity,X3)) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h18,h21]) ).
cnf(t4509,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(step,[status(thm)],[t168,t258]) ).
cnf(t265,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t4509]) ).
cnf(f5,axiom,
sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
sum(X0,additive_inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t27,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(t4510,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t27,t258]) ).
cnf(t279,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t4510]) ).
cnf(t281,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t265,t279]) ).
cnf(t4525,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t281,t258]) ).
cnf(t818,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t4525]) ).
cnf(t820,plain,
additive_inverse(additive_inverse(X1)) = add(X1,additive_identity),
inference(cp,[status(thm)],[t818,t279]) ).
cnf(t4526,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t820,t257]) ).
cnf(t839,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t4526]) ).
cnf(t841,plain,
X1 = add(additive_inverse(X2),add(X2,X1)),
inference(cp,[status(thm)],[t818,t839]) ).
cnf(t869,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(orient,[status(thm)],[t841]) ).
cnf(t82,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t268,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t82]) ).
cnf(t872,plain,
add(X1,additive_inverse(add(X2,X1))) = add(additive_inverse(X2),additive_identity),
inference(cp,[status(thm)],[t869,t268]) ).
cnf(t4527,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(step,[status(thm)],[t872,t257]) ).
cnf(t921,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t4527]) ).
cnf(t928,plain,
additive_inverse(add(X1,X2)) = add(additive_inverse(X2),additive_inverse(X1)),
inference(cp,[status(thm)],[t869,t921]) ).
cnf(t943,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(orient,[status(thm)],[t928]) ).
cnf(t951,plain,
true = product(additive_inverse(add(X1,X1)),additive_identity,multiply(additive_inverse(X1),additive_identity)),
inference(cp,[status(thm)],[t493,t943]) ).
cnf(t3866,plain,
product(additive_inverse(add(X1,X1)),additive_identity,multiply(additive_inverse(X1),additive_identity)) = true,
inference(orient,[status(thm)],[t951]) ).
cnf(t3881,plain,
multiply(additive_inverse(X1),additive_identity) = ifeq(true,true,multiply(additive_inverse(add(X1,X1)),additive_identity),multiply(additive_inverse(X1),additive_identity)),
inference(cp,[status(thm)],[t3859,t3866]) ).
cnf(t4560,plain,
multiply(additive_inverse(X1),additive_identity) = multiply(additive_inverse(add(X1,X1)),additive_identity),
inference(step,[status(thm)],[t3881,t259]) ).
cnf(t3904,plain,
multiply(additive_inverse(add(X1,X1)),additive_identity) = multiply(additive_inverse(X1),additive_identity),
inference(orient,[status(thm)],[t4560]) ).
cnf(t3922,plain,
multiply(add(additive_inverse(add(X1,X1)),X2),additive_identity) = add(multiply(additive_inverse(X1),additive_identity),multiply(X2,additive_identity)),
inference(cp,[status(thm)],[t283,t3904]) ).
cnf(t4566,plain,
multiply(add(additive_inverse(add(X1,X1)),X2),additive_identity) = multiply(add(additive_inverse(X1),X2),additive_identity),
inference(step,[status(thm)],[t3922,t283]) ).
cnf(t4403,plain,
multiply(add(additive_inverse(add(X1,X1)),X2),additive_identity) = multiply(add(additive_inverse(X1),X2),additive_identity),
inference(orient,[status(thm)],[t4566]) ).
cnf(t4420,plain,
multiply(add(additive_inverse(X1),add(additive_inverse(additive_inverse(add(X1,X1))),X2)),additive_identity) = multiply(X2,additive_identity),
inference(cp,[status(thm)],[t4403,t818]) ).
cnf(t949,plain,
add(additive_inverse(X1),add(additive_inverse(X2),X3)) = add(additive_inverse(add(X2,X1)),X3),
inference(cp,[status(thm)],[t265,t943]) ).
cnf(t1921,plain,
add(additive_inverse(X1),add(additive_inverse(X2),X3)) = add(additive_inverse(add(X2,X1)),X3),
inference(orient,[status(thm)],[t949]) ).
cnf(t4567,plain,
multiply(add(additive_inverse(add(additive_inverse(add(X1,X1)),X1)),X2),additive_identity) = multiply(X2,additive_identity),
inference(step,[status(thm)],[t4420,t1921]) ).
cnf(t948,plain,
additive_inverse(add(additive_inverse(X1),X2)) = add(additive_inverse(X2),X1),
inference(cp,[status(thm)],[t943,t839]) ).
cnf(t983,plain,
additive_inverse(add(additive_inverse(X1),X2)) = add(additive_inverse(X2),X1),
inference(orient,[status(thm)],[t948]) ).
cnf(t4568,plain,
multiply(add(add(additive_inverse(X1),add(X1,X1)),X2),additive_identity) = multiply(X2,additive_identity),
inference(step,[status(thm)],[t4567,t983]) ).
cnf(h20,plain,
sum(add(V0,additive_identity),V1,add(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi0,hi3]) ).
cnf(f8,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h17,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3]) ).
cnf(t50,plain,
add(X1,add(X2,additive_identity)) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,h17,h20]) ).
cnf(t4508,plain,
add(X1,X2) = add(X2,X1),
inference(step,[status(thm)],[t50,t257]) ).
cnf(t264,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t4508]) ).
cnf(t267,plain,
add(X1,add(X2,X3)) = add(add(X2,X1),X3),
inference(cp,[status(thm)],[t265,t264]) ).
cnf(t4555,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(step,[status(thm)],[t267,t265]) ).
cnf(t3381,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(orient,[status(thm)],[t4555]) ).
cnf(t4569,plain,
multiply(add(add(X1,add(additive_inverse(X1),X1)),X2),additive_identity) = multiply(X2,additive_identity),
inference(step,[status(thm)],[t4568,t3381]) ).
cnf(t4570,plain,
multiply(add(X1,X2),additive_identity) = multiply(X2,additive_identity),
inference(step,[status(thm)],[t4569,t818]) ).
cnf(t4451,plain,
multiply(add(X1,X2),additive_identity) = multiply(X2,additive_identity),
inference(orient,[status(thm)],[t4570]) ).
cnf(t4457,plain,
multiply(additive_identity,additive_identity) = multiply(X1,additive_identity),
inference(cp,[status(thm)],[t4451,t257]) ).
cnf(h2,plain,
sum(multiply(additive_identity,V0),multiply(V1,V0),multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi0,hi2]) ).
cnf(t77,plain,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(hyper_resolution,[status(thm)],[hi15,h2,h16]) ).
cnf(t319,plain,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(orient,[status(thm)],[t77]) ).
cnf(t324,plain,
multiply(additive_identity,add(add(X1,X1),X2)) = add(multiply(additive_identity,X1),multiply(additive_identity,X2)),
inference(cp,[status(thm)],[t287,t319]) ).
cnf(t4534,plain,
multiply(additive_identity,add(X1,add(X1,X2))) = add(multiply(additive_identity,X1),multiply(additive_identity,X2)),
inference(step,[status(thm)],[t324,t265]) ).
cnf(t4535,plain,
multiply(additive_identity,add(X1,add(X1,X2))) = multiply(additive_identity,add(X1,X2)),
inference(step,[status(thm)],[t4534,t287]) ).
cnf(t1422,plain,
multiply(additive_identity,add(X1,add(X1,X2))) = multiply(additive_identity,add(X1,X2)),
inference(orient,[status(thm)],[t4535]) ).
cnf(t822,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t818,t264]) ).
cnf(t842,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t822]) ).
cnf(t1423,plain,
multiply(additive_identity,add(X1,additive_inverse(X1))) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t1422,t842]) ).
cnf(t4536,plain,
multiply(additive_identity,additive_identity) = multiply(additive_identity,X1),
inference(step,[status(thm)],[t1423,t279]) ).
cnf(t1444,plain,
multiply(additive_identity,additive_identity) = multiply(additive_identity,X1),
inference(orient,[status(thm)],[t4536]) ).
cnf(t1453,plain,
multiply(additive_identity,X1) = multiply(additive_identity,X2),
inference(cp,[status(thm)],[t1444,t1444]) ).
cnf(t1469,plain,
multiply(additive_identity,X1) = multiply(additive_identity,X2),
inference(orient,[status(thm)],[t1453]) ).
cnf(t1477,plain,
multiply(add(additive_identity,X1),X2) = add(multiply(additive_identity,X3),multiply(X1,X2)),
inference(cp,[status(thm)],[t283,t1469]) ).
cnf(t4538,plain,
multiply(X1,X2) = add(multiply(additive_identity,X3),multiply(X1,X2)),
inference(step,[status(thm)],[t1477,t258]) ).
cnf(t1527,plain,
add(multiply(additive_identity,X1),multiply(X2,X3)) = multiply(X2,X3),
inference(orient,[status(thm)],[t4538]) ).
cnf(t1547,plain,
additive_inverse(multiply(additive_identity,X1)) = add(multiply(X2,X3),additive_inverse(multiply(X2,X3))),
inference(cp,[status(thm)],[t921,t1527]) ).
cnf(t4539,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(step,[status(thm)],[t1547,t279]) ).
cnf(t1564,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(orient,[status(thm)],[t4539]) ).
cnf(t1573,plain,
multiply(additive_identity,X1) = additive_inverse(additive_identity),
inference(cp,[status(thm)],[t839,t1564]) ).
cnf(f4,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f4_nnf,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
sum(additive_inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h51,plain,
sum(additive_inverse(additive_identity),additive_identity,additive_identity) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi1,hi4]) ).
cnf(t32,plain,
add(additive_identity,add(additive_inverse(additive_identity),additive_identity)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,h51,h23]) ).
cnf(t4513,plain,
add(additive_inverse(additive_identity),additive_identity) = additive_identity,
inference(step,[status(thm)],[t32,t258]) ).
cnf(t4514,plain,
additive_inverse(additive_identity) = additive_identity,
inference(step,[status(thm)],[t4513,t257]) ).
cnf(t292,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t4514]) ).
cnf(t4540,plain,
multiply(additive_identity,X1) = additive_identity,
inference(step,[status(thm)],[t1573,t292]) ).
cnf(t1589,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t4540]) ).
cnf(t4571,plain,
additive_identity = multiply(X1,additive_identity),
inference(step,[status(thm)],[t4457,t1589]) ).
cnf(t4477,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t4571]) ).
cnf(t4479,plain,
true = product(X1,additive_identity,additive_identity),
inference(cp,[status(thm)],[t472,t4477]) ).
cnf(t4484,plain,
product(X1,additive_identity,additive_identity) = true,
inference(orient,[status(thm)],[t4479]) ).
cnf(f17,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_0_is_0) ).
fof(f17_nnf,plain,
~ product(a,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
~ product(a,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(goal_0,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4484]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.42 % Computer : n004.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8046.5625MB
% 0.19/0.42 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Thu Sep 24 07:40:05 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.07/5.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.07/5.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------