%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 12:59:33 PM UTC 2026
% Result : Unsatisfiable 11.63s 6.70s
% Output : Proof 11.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 20
% Syntax : Number of formulae : 255 ( 231 unt; 0 def)
% Number of atoms : 323 ( 190 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 142 ( 74 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 331 ( 15 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
fof(f15_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(product(X0,X3,X5),true,ifeq(product(X2,X4,X6),true,sum(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f0,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f0_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f1_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h5,plain,
sum(multiply(V0,V1),V2,multiply(add(V0,V2),add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi0,hi0,hi1,hi1]) ).
cnf(f2,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0]) ).
cnf(f20,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f20_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t220,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(hyper_resolution,[status(thm)],[hi20,h1,h5]) ).
cnf(t394,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(orient,[status(thm)],[t220]) ).
cnf(f13,axiom,
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity6) ).
fof(f13_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X3,X4),true,ifeq(product(X1,X3,X5),true,ifeq(product(X2,X4,X6),true,sum(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h13,plain,
sum(V0,multiply(V1,V2),multiply(add(V0,V1),add(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi0,hi0,hi1,hi1]) ).
cnf(t218,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h13]) ).
cnf(t465,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t218]) ).
cnf(f17,axiom,
sum(X,inverse(X),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse2) ).
fof(f17_nnf,plain,
! [X] : sum(X,inverse(X),multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] : sum(X,inverse(X),multiplicative_identity),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
sum(X0,inverse(X0),multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t14,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi17]) ).
cnf(t726,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t14]) ).
cnf(t728,plain,
add(inverse(X1),multiply(X1,X2)) = multiply(multiplicative_identity,add(X2,inverse(X1))),
inference(cp,[status(thm)],[t394,t726]) ).
cnf(f21,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f21_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(f6,axiom,
product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f6_nnf,plain,
! [X] : product(multiplicative_identity,X,X),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : product(multiplicative_identity,X,X),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
product(multiplicative_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t13,plain,
multiply(multiplicative_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi6]) ).
cnf(t257,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t20205,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(step,[status(thm)],[t728,t257]) ).
cnf(t16191,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(orient,[status(thm)],[t20205]) ).
cnf(f23,hypothesis,
sum(x,y_plus_z,x__plus_y_plus_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus__y_plus_z) ).
fof(f23_nnf,plain,
sum(x,y_plus_z,x__plus_y_plus_z),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
sum(x,y_plus_z,x__plus_y_plus_z),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,axiom,
sum(x,y_plus_z,x__plus_y_plus_z) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t5,plain,
add(x,y_plus_z) = x__plus_y_plus_z,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi23]) ).
cnf(t30,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h1]) ).
cnf(t534,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t30]) ).
cnf(t19863,plain,
add(y_plus_z,x) = x__plus_y_plus_z,
inference(step,[status(thm)],[t5,t534]) ).
cnf(t809,plain,
add(y_plus_z,x) = x__plus_y_plus_z,
inference(orient,[status(thm)],[t19863]) ).
cnf(t810,plain,
add(x,multiply(y_plus_z,X1)) = multiply(x__plus_y_plus_z,add(X1,x)),
inference(cp,[status(thm)],[t394,t809]) ).
cnf(t4799,plain,
add(x,multiply(y_plus_z,X1)) = multiply(x__plus_y_plus_z,add(X1,x)),
inference(orient,[status(thm)],[t810]) ).
cnf(f25,hypothesis,
sum(x_plus_y,z,x_plus_y__plus_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y__plus_z) ).
fof(f25_nnf,plain,
sum(x_plus_y,z,x_plus_y__plus_z),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
sum(x_plus_y,z,x_plus_y__plus_z),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,axiom,
sum(x_plus_y,z,x_plus_y__plus_z) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t10,plain,
add(z,x_plus_y) = x_plus_y__plus_z,
inference(hyper_resolution,[status(thm)],[hi20,hi25,h1]) ).
cnf(t791,plain,
add(z,x_plus_y) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t10]) ).
cnf(t795,plain,
add(z,multiply(X1,x_plus_y)) = multiply(add(z,X1),x_plus_y__plus_z),
inference(cp,[status(thm)],[t465,t791]) ).
cnf(t4593,plain,
add(z,multiply(X1,x_plus_y)) = multiply(add(z,X1),x_plus_y__plus_z),
inference(orient,[status(thm)],[t795]) ).
cnf(f4,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f4_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3,plain,
sum(multiply(additive_identity,V0),V1,multiply(V1,add(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi4,hi0,hi1,hi1]) ).
cnf(t155,plain,
multiply(X1,add(X2,X1)) = add(multiply(additive_identity,X2),X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h3]) ).
cnf(t286,plain,
add(multiply(additive_identity,X1),X2) = multiply(X2,add(X1,X2)),
inference(orient,[status(thm)],[t155]) ).
cnf(f11,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(f11_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)],[f11]) ).
fof(f11_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)],[f11_nnf]) ).
cnf(c11,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)],[f11_sk]) ).
cnf(hi11,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)],[c11]) ).
cnf(h21,plain,
product(V0,V1,add(multiply(additive_identity,V1),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi1,hi1,hi4,hi0]) ).
cnf(t150,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(hyper_resolution,[status(thm)],[hi21,hi1,h21]) ).
cnf(t268,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(orient,[status(thm)],[t150]) ).
cnf(f18,axiom,
product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f18_nnf,plain,
! [X] : product(inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X] : product(inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
product(inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t17,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi18]) ).
cnf(t527,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(orient,[status(thm)],[t17]) ).
cnf(t529,plain,
multiply(inverse(X1),X1) = add(multiply(additive_identity,X1),additive_identity),
inference(cp,[status(thm)],[t268,t527]) ).
cnf(t19879,plain,
additive_identity = add(multiply(additive_identity,X1),additive_identity),
inference(step,[status(thm)],[t529,t527]) ).
cnf(f5,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t2,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi5]) ).
cnf(t258,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t19880,plain,
additive_identity = multiply(additive_identity,X1),
inference(step,[status(thm)],[t19879,t258]) ).
cnf(t3109,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t19880]) ).
cnf(t19889,plain,
add(additive_identity,X2) = multiply(X2,add(X1,X2)),
inference(step,[status(thm)],[t286,t3109]) ).
cnf(f7,axiom,
product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f7_nnf,plain,
! [X] : product(X,multiplicative_identity,X),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] : product(X,multiplicative_identity,X),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
product(X0,multiplicative_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t84,plain,
add(multiply(additive_identity,multiplicative_identity),multiply(X1,multiplicative_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi21,hi7,h21]) ).
cnf(t12,plain,
multiply(X1,multiplicative_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi7]) ).
cnf(t256,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t12]) ).
cnf(t19856,plain,
add(additive_identity,multiply(X1,multiplicative_identity)) = X1,
inference(step,[status(thm)],[t84,t256]) ).
cnf(t19857,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t19856,t256]) ).
cnf(t262,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t19857]) ).
cnf(t19890,plain,
X2 = multiply(X2,add(X1,X2)),
inference(step,[status(thm)],[t19889,t262]) ).
cnf(t3131,plain,
X2 = multiply(X2,add(X1,X2)),
inference(rw,[status(thm)],[t19890]) ).
cnf(t3491,plain,
multiply(X1,add(X2,X1)) = X1,
inference(orient,[status(thm)],[t3131]) ).
cnf(t3496,plain,
X1 = multiply(X1,add(X1,X2)),
inference(cp,[status(thm)],[t3491,t534]) ).
cnf(t3699,plain,
multiply(X1,add(X1,X2)) = X1,
inference(orient,[status(thm)],[t3496]) ).
cnf(f24,hypothesis,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
fof(f24_nnf,plain,
sum(x,y,x_plus_y),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
sum(x,y,x_plus_y),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(hi24,axiom,
sum(x,y,x_plus_y) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t4,plain,
add(x,y) = x_plus_y,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi24]) ).
cnf(t19864,plain,
add(y,x) = x_plus_y,
inference(step,[status(thm)],[t4,t534]) ).
cnf(t818,plain,
add(y,x) = x_plus_y,
inference(orient,[status(thm)],[t19864]) ).
cnf(t3701,plain,
y = multiply(y,x_plus_y),
inference(cp,[status(thm)],[t3699,t818]) ).
cnf(t3730,plain,
multiply(y,x_plus_y) = y,
inference(orient,[status(thm)],[t3701]) ).
cnf(t4594,plain,
multiply(add(z,y),x_plus_y__plus_z) = add(z,y),
inference(cp,[status(thm)],[t4593,t3730]) ).
cnf(f22,hypothesis,
sum(y,z,y_plus_z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',y_plus_z) ).
fof(f22_nnf,plain,
sum(y,z,y_plus_z),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
sum(y,z,y_plus_z),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,axiom,
sum(y,z,y_plus_z) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t11,plain,
add(z,y) = y_plus_z,
inference(hyper_resolution,[status(thm)],[hi20,hi22,h1]) ).
cnf(t800,plain,
add(z,y) = y_plus_z,
inference(orient,[status(thm)],[t11]) ).
cnf(t19956,plain,
multiply(y_plus_z,x_plus_y__plus_z) = add(z,y),
inference(step,[status(thm)],[t4594,t800]) ).
cnf(t19957,plain,
multiply(y_plus_z,x_plus_y__plus_z) = y_plus_z,
inference(step,[status(thm)],[t19956,t800]) ).
cnf(t4614,plain,
multiply(y_plus_z,x_plus_y__plus_z) = y_plus_z,
inference(orient,[status(thm)],[t19957]) ).
cnf(t4804,plain,
multiply(x__plus_y_plus_z,add(x_plus_y__plus_z,x)) = add(x,y_plus_z),
inference(cp,[status(thm)],[t4799,t4614]) ).
cnf(t19969,plain,
multiply(x__plus_y_plus_z,add(x_plus_y__plus_z,x)) = add(y_plus_z,x),
inference(step,[status(thm)],[t4804,t534]) ).
cnf(t19970,plain,
multiply(x__plus_y_plus_z,add(x_plus_y__plus_z,x)) = x__plus_y_plus_z,
inference(step,[status(thm)],[t19969,t809]) ).
cnf(t4829,plain,
multiply(x__plus_y_plus_z,add(x_plus_y__plus_z,x)) = x__plus_y_plus_z,
inference(orient,[status(thm)],[t19970]) ).
cnf(t730,plain,
add(X1,multiply(inverse(X1),X2)) = multiply(multiplicative_identity,add(X1,X2)),
inference(cp,[status(thm)],[t465,t726]) ).
cnf(t19991,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(step,[status(thm)],[t730,t257]) ).
cnf(t5237,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(orient,[status(thm)],[t19991]) ).
cnf(t5243,plain,
add(X1,X1) = add(X1,additive_identity),
inference(cp,[status(thm)],[t5237,t527]) ).
cnf(t19992,plain,
add(X1,X1) = X1,
inference(step,[status(thm)],[t5243,t258]) ).
cnf(t5267,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t19992]) ).
cnf(t5268,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,X1)),
inference(cp,[status(thm)],[t394,t5267]) ).
cnf(t19994,plain,
add(X1,multiply(X1,X2)) = X1,
inference(step,[status(thm)],[t5268,t3491]) ).
cnf(t5330,plain,
add(X1,multiply(X1,X2)) = X1,
inference(orient,[status(thm)],[t19994]) ).
cnf(t792,plain,
add(x_plus_y,multiply(z,X1)) = multiply(x_plus_y__plus_z,add(X1,x_plus_y)),
inference(cp,[status(thm)],[t394,t791]) ).
cnf(t4467,plain,
add(x_plus_y,multiply(z,X1)) = multiply(x_plus_y__plus_z,add(X1,x_plus_y)),
inference(orient,[status(thm)],[t792]) ).
cnf(f19,axiom,
product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse2) ).
fof(f19_nnf,plain,
! [X] : product(X,inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] : product(X,inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
product(X0,inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t16,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi19]) ).
cnf(t299,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t16]) ).
cnf(t4474,plain,
multiply(x_plus_y__plus_z,add(inverse(z),x_plus_y)) = add(x_plus_y,additive_identity),
inference(cp,[status(thm)],[t4467,t299]) ).
cnf(t19949,plain,
multiply(x_plus_y__plus_z,add(x_plus_y,inverse(z))) = add(x_plus_y,additive_identity),
inference(step,[status(thm)],[t4474,t534]) ).
cnf(t19950,plain,
multiply(x_plus_y__plus_z,add(x_plus_y,inverse(z))) = x_plus_y,
inference(step,[status(thm)],[t19949,t258]) ).
cnf(t4495,plain,
multiply(x_plus_y__plus_z,add(x_plus_y,inverse(z))) = x_plus_y,
inference(orient,[status(thm)],[t19950]) ).
cnf(t5342,plain,
x_plus_y__plus_z = add(x_plus_y__plus_z,x_plus_y),
inference(cp,[status(thm)],[t5330,t4495]) ).
cnf(t5398,plain,
add(x_plus_y__plus_z,x_plus_y) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t5342]) ).
cnf(t5403,plain,
add(x_plus_y__plus_z,multiply(x_plus_y,X1)) = multiply(x_plus_y__plus_z,add(x_plus_y__plus_z,X1)),
inference(cp,[status(thm)],[t465,t5398]) ).
cnf(t20007,plain,
add(x_plus_y__plus_z,multiply(x_plus_y,X1)) = x_plus_y__plus_z,
inference(step,[status(thm)],[t5403,t3699]) ).
cnf(t6227,plain,
add(x_plus_y__plus_z,multiply(x_plus_y,X1)) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t20007]) ).
cnf(t819,plain,
add(x,multiply(y,X1)) = multiply(x_plus_y,add(X1,x)),
inference(cp,[status(thm)],[t394,t818]) ).
cnf(t5068,plain,
add(x,multiply(y,X1)) = multiply(x_plus_y,add(X1,x)),
inference(orient,[status(thm)],[t819]) ).
cnf(t5075,plain,
multiply(x_plus_y,add(inverse(y),x)) = add(x,additive_identity),
inference(cp,[status(thm)],[t5068,t299]) ).
cnf(t19984,plain,
multiply(x_plus_y,add(x,inverse(y))) = add(x,additive_identity),
inference(step,[status(thm)],[t5075,t534]) ).
cnf(t19985,plain,
multiply(x_plus_y,add(x,inverse(y))) = x,
inference(step,[status(thm)],[t19984,t258]) ).
cnf(t5093,plain,
multiply(x_plus_y,add(x,inverse(y))) = x,
inference(orient,[status(thm)],[t19985]) ).
cnf(t6229,plain,
x_plus_y__plus_z = add(x_plus_y__plus_z,x),
inference(cp,[status(thm)],[t6227,t5093]) ).
cnf(t6244,plain,
add(x_plus_y__plus_z,x) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t6229]) ).
cnf(t20010,plain,
multiply(x__plus_y_plus_z,x_plus_y__plus_z) = x__plus_y_plus_z,
inference(step,[status(thm)],[t4829,t6244]) ).
cnf(t6260,plain,
multiply(x__plus_y_plus_z,x_plus_y__plus_z) = x__plus_y_plus_z,
inference(rw,[status(thm)],[t20010]) ).
cnf(t6281,plain,
multiply(x__plus_y_plus_z,x_plus_y__plus_z) = x__plus_y_plus_z,
inference(orient,[status(thm)],[t6260]) ).
cnf(t16273,plain,
add(x_plus_y__plus_z,inverse(x__plus_y_plus_z)) = add(inverse(x__plus_y_plus_z),x__plus_y_plus_z),
inference(cp,[status(thm)],[t16191,t6281]) ).
cnf(t20208,plain,
add(x_plus_y__plus_z,inverse(x__plus_y_plus_z)) = add(x__plus_y_plus_z,inverse(x__plus_y_plus_z)),
inference(step,[status(thm)],[t16273,t534]) ).
cnf(t20209,plain,
add(x_plus_y__plus_z,inverse(x__plus_y_plus_z)) = multiplicative_identity,
inference(step,[status(thm)],[t20208,t726]) ).
cnf(t16463,plain,
add(x_plus_y__plus_z,inverse(x__plus_y_plus_z)) = multiplicative_identity,
inference(orient,[status(thm)],[t20209]) ).
cnf(t16468,plain,
add(x_plus_y__plus_z,multiply(inverse(x__plus_y_plus_z),X1)) = multiply(multiplicative_identity,add(x_plus_y__plus_z,X1)),
inference(cp,[status(thm)],[t465,t16463]) ).
cnf(t20285,plain,
add(x_plus_y__plus_z,multiply(inverse(x__plus_y_plus_z),X1)) = add(x_plus_y__plus_z,X1),
inference(step,[status(thm)],[t16468,t257]) ).
cnf(t18964,plain,
add(x_plus_y__plus_z,multiply(inverse(x__plus_y_plus_z),X1)) = add(x_plus_y__plus_z,X1),
inference(orient,[status(thm)],[t20285]) ).
cnf(t18969,plain,
add(x_plus_y__plus_z,x__plus_y_plus_z) = add(x_plus_y__plus_z,additive_identity),
inference(cp,[status(thm)],[t18964,t527]) ).
cnf(t20286,plain,
add(x_plus_y__plus_z,x__plus_y_plus_z) = x_plus_y__plus_z,
inference(step,[status(thm)],[t18969,t258]) ).
cnf(t19005,plain,
add(x_plus_y__plus_z,x__plus_y_plus_z) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t20286]) ).
cnf(t19006,plain,
add(x__plus_y_plus_z,multiply(x_plus_y__plus_z,X1)) = multiply(x_plus_y__plus_z,add(X1,x__plus_y_plus_z)),
inference(cp,[status(thm)],[t394,t19005]) ).
cnf(t19714,plain,
add(x__plus_y_plus_z,multiply(x_plus_y__plus_z,X1)) = multiply(x_plus_y__plus_z,add(X1,x__plus_y_plus_z)),
inference(orient,[status(thm)],[t19006]) ).
cnf(t19745,plain,
multiply(x_plus_y__plus_z,add(inverse(x_plus_y__plus_z),x__plus_y_plus_z)) = add(x__plus_y_plus_z,additive_identity),
inference(cp,[status(thm)],[t19714,t299]) ).
cnf(t20296,plain,
multiply(x_plus_y__plus_z,add(x__plus_y_plus_z,inverse(x_plus_y__plus_z))) = add(x__plus_y_plus_z,additive_identity),
inference(step,[status(thm)],[t19745,t534]) ).
cnf(t794,plain,
add(z,multiply(x_plus_y,X1)) = multiply(x_plus_y__plus_z,add(z,X1)),
inference(cp,[status(thm)],[t465,t791]) ).
cnf(t4567,plain,
add(z,multiply(x_plus_y,X1)) = multiply(x_plus_y__plus_z,add(z,X1)),
inference(orient,[status(thm)],[t794]) ).
cnf(t811,plain,
add(x,multiply(X1,y_plus_z)) = multiply(add(X1,x),x__plus_y_plus_z),
inference(cp,[status(thm)],[t394,t809]) ).
cnf(t4883,plain,
add(x,multiply(X1,y_plus_z)) = multiply(add(X1,x),x__plus_y_plus_z),
inference(orient,[status(thm)],[t811]) ).
cnf(t3495,plain,
y = multiply(y,y_plus_z),
inference(cp,[status(thm)],[t3491,t800]) ).
cnf(t3545,plain,
multiply(y,y_plus_z) = y,
inference(orient,[status(thm)],[t3495]) ).
cnf(t4888,plain,
multiply(add(y,x),x__plus_y_plus_z) = add(x,y),
inference(cp,[status(thm)],[t4883,t3545]) ).
cnf(t19974,plain,
multiply(x_plus_y,x__plus_y_plus_z) = add(x,y),
inference(step,[status(thm)],[t4888,t818]) ).
cnf(t19975,plain,
multiply(x_plus_y,x__plus_y_plus_z) = add(y,x),
inference(step,[status(thm)],[t19974,t534]) ).
cnf(t19976,plain,
multiply(x_plus_y,x__plus_y_plus_z) = x_plus_y,
inference(step,[status(thm)],[t19975,t818]) ).
cnf(t4908,plain,
multiply(x_plus_y,x__plus_y_plus_z) = x_plus_y,
inference(orient,[status(thm)],[t19976]) ).
cnf(t4909,plain,
multiply(x_plus_y__plus_z,add(z,x__plus_y_plus_z)) = add(z,x_plus_y),
inference(cp,[status(thm)],[t4567,t4908]) ).
cnf(t19977,plain,
multiply(x_plus_y__plus_z,add(z,x__plus_y_plus_z)) = x_plus_y__plus_z,
inference(step,[status(thm)],[t4909,t791]) ).
cnf(t4914,plain,
multiply(x_plus_y__plus_z,add(z,x__plus_y_plus_z)) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t19977]) ).
cnf(t812,plain,
add(y_plus_z,multiply(x,X1)) = multiply(x__plus_y_plus_z,add(y_plus_z,X1)),
inference(cp,[status(thm)],[t465,t809]) ).
cnf(t4972,plain,
add(y_plus_z,multiply(x,X1)) = multiply(x__plus_y_plus_z,add(y_plus_z,X1)),
inference(orient,[status(thm)],[t812]) ).
cnf(t4977,plain,
multiply(x__plus_y_plus_z,add(y_plus_z,inverse(x))) = add(y_plus_z,additive_identity),
inference(cp,[status(thm)],[t4972,t299]) ).
cnf(t19982,plain,
multiply(x__plus_y_plus_z,add(y_plus_z,inverse(x))) = y_plus_z,
inference(step,[status(thm)],[t4977,t258]) ).
cnf(t4998,plain,
multiply(x__plus_y_plus_z,add(y_plus_z,inverse(x))) = y_plus_z,
inference(orient,[status(thm)],[t19982]) ).
cnf(t5334,plain,
x__plus_y_plus_z = add(x__plus_y_plus_z,y_plus_z),
inference(cp,[status(thm)],[t5330,t4998]) ).
cnf(t19995,plain,
x__plus_y_plus_z = add(y_plus_z,x__plus_y_plus_z),
inference(step,[status(thm)],[t5334,t534]) ).
cnf(t5371,plain,
add(y_plus_z,x__plus_y_plus_z) = x__plus_y_plus_z,
inference(orient,[status(thm)],[t19995]) ).
cnf(t5372,plain,
add(x__plus_y_plus_z,multiply(y_plus_z,X1)) = multiply(x__plus_y_plus_z,add(X1,x__plus_y_plus_z)),
inference(cp,[status(thm)],[t394,t5371]) ).
cnf(t19999,plain,
add(x__plus_y_plus_z,multiply(y_plus_z,X1)) = x__plus_y_plus_z,
inference(step,[status(thm)],[t5372,t3491]) ).
cnf(t5881,plain,
add(x__plus_y_plus_z,multiply(y_plus_z,X1)) = x__plus_y_plus_z,
inference(orient,[status(thm)],[t19999]) ).
cnf(t803,plain,
add(z,multiply(y,X1)) = multiply(y_plus_z,add(z,X1)),
inference(cp,[status(thm)],[t465,t800]) ).
cnf(t4742,plain,
add(z,multiply(y,X1)) = multiply(y_plus_z,add(z,X1)),
inference(orient,[status(thm)],[t803]) ).
cnf(t4746,plain,
multiply(y_plus_z,add(z,inverse(y))) = add(z,additive_identity),
inference(cp,[status(thm)],[t4742,t299]) ).
cnf(t19966,plain,
multiply(y_plus_z,add(z,inverse(y))) = z,
inference(step,[status(thm)],[t4746,t258]) ).
cnf(t4764,plain,
multiply(y_plus_z,add(z,inverse(y))) = z,
inference(orient,[status(thm)],[t19966]) ).
cnf(t5882,plain,
x__plus_y_plus_z = add(x__plus_y_plus_z,z),
inference(cp,[status(thm)],[t5881,t4764]) ).
cnf(t20000,plain,
x__plus_y_plus_z = add(z,x__plus_y_plus_z),
inference(step,[status(thm)],[t5882,t534]) ).
cnf(t5904,plain,
add(z,x__plus_y_plus_z) = x__plus_y_plus_z,
inference(orient,[status(thm)],[t20000]) ).
cnf(t20003,plain,
multiply(x_plus_y__plus_z,x__plus_y_plus_z) = x_plus_y__plus_z,
inference(step,[status(thm)],[t4914,t5904]) ).
cnf(t5920,plain,
multiply(x_plus_y__plus_z,x__plus_y_plus_z) = x_plus_y__plus_z,
inference(rw,[status(thm)],[t20003]) ).
cnf(t5942,plain,
multiply(x_plus_y__plus_z,x__plus_y_plus_z) = x_plus_y__plus_z,
inference(orient,[status(thm)],[t5920]) ).
cnf(t16302,plain,
add(x__plus_y_plus_z,inverse(x_plus_y__plus_z)) = add(inverse(x_plus_y__plus_z),x_plus_y__plus_z),
inference(cp,[status(thm)],[t16191,t5942]) ).
cnf(t20210,plain,
add(x__plus_y_plus_z,inverse(x_plus_y__plus_z)) = add(x_plus_y__plus_z,inverse(x_plus_y__plus_z)),
inference(step,[status(thm)],[t16302,t534]) ).
cnf(t20211,plain,
add(x__plus_y_plus_z,inverse(x_plus_y__plus_z)) = multiplicative_identity,
inference(step,[status(thm)],[t20210,t726]) ).
cnf(t16532,plain,
add(x__plus_y_plus_z,inverse(x_plus_y__plus_z)) = multiplicative_identity,
inference(orient,[status(thm)],[t20211]) ).
cnf(t20297,plain,
multiply(x_plus_y__plus_z,multiplicative_identity) = add(x__plus_y_plus_z,additive_identity),
inference(step,[status(thm)],[t20296,t16532]) ).
cnf(t20298,plain,
x_plus_y__plus_z = add(x__plus_y_plus_z,additive_identity),
inference(step,[status(thm)],[t20297,t256]) ).
cnf(t20299,plain,
x_plus_y__plus_z = x__plus_y_plus_z,
inference(step,[status(thm)],[t20298,t258]) ).
cnf(t19785,plain,
x__plus_y_plus_z = x_plus_y__plus_z,
inference(orient,[status(thm)],[t20299]) ).
cnf(f26,negated_conjecture,
x__plus_y_plus_z != x_plus_y__plus_z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equality) ).
fof(f26_nnf,plain,
x__plus_y_plus_z != x_plus_y__plus_z,
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
x__plus_y_plus_z != x_plus_y__plus_z,
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
x__plus_y_plus_z != x_plus_y__plus_z,
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
x_plus_y__plus_z != x__plus_y_plus_z,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
x_plus_y__plus_z != x_plus_y__plus_z,
inference(rw,[status(thm)],[goal_0,t19785]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 06:24:34 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.63/6.70 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.63/6.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------