%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:37:24 PM UTC 2026
% Result : Unsatisfiable 35.84s 5.32s
% Output : Proof 35.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 88
% Number of leaves : 18
% Syntax : Number of formulae : 299 ( 259 unt; 0 def)
% Number of atoms : 419 ( 235 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 246 ( 126 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 530 ( 14 sgn 130 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t30,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t476,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(f10,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f10_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X0,X4,X5),true,product(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h5,plain,
product(multiply(V0,V1),V2,multiply(V0,multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi2,hi2,hi2]) ).
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(hi16,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f17,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f17_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
product(X0,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t125,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(hyper_resolution,[status(thm)],[hi16,hi17,h5]) ).
cnf(t425,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(orient,[status(thm)],[t125]) ).
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(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(h14,plain,
product(V0,V1,add(multiply(V0,V1),multiply(V0,additive_identity))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2,hi2,hi1,hi3]) ).
cnf(f9,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f9_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X2,X3,X5),true,product(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h6,plain,
product(V0,multiply(V1,V2),multiply(multiply(V0,V1),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi2,hi2,hi2]) ).
cnf(t226,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X1,additive_identity)) = multiply(multiply(X1,X2),X3),
inference(hyper_resolution,[status(thm)],[hi16,h6,h14]) ).
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(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,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(t219,plain,
add(multiply(X1,X2),add(additive_identity,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h16,h21]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,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(t110,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,h17,h18]) ).
cnf(t298,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(orient,[status(thm)],[t110]) ).
cnf(t6419,plain,
add(additive_identity,add(multiply(X1,X3),multiply(X1,X2))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t219,t298]) ).
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(t2,plain,
add(additive_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi0,hi3]) ).
cnf(t262,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t6420,plain,
add(multiply(X1,X3),multiply(X1,X2)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t6419,t262]) ).
cnf(t383,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X3,X2)),
inference(orient,[status(thm)],[t6420]) ).
cnf(t6423,plain,
multiply(X1,add(additive_identity,multiply(X2,X3))) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t226,t383]) ).
cnf(t6424,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t6423,t262]) ).
cnf(t410,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t6424]) ).
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(h11,plain,
product(V0,V1,add(multiply(additive_identity,V1),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi0,hi3]) ).
cnf(f18,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f18_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t64,plain,
add(multiply(additive_identity,b),multiply(a,b)) = c,
inference(hyper_resolution,[status(thm)],[hi16,hi18,h11]) ).
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(t220,plain,
add(multiply(X1,X2),add(additive_identity,multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi15,h12,h21]) ).
cnf(t6416,plain,
add(additive_identity,add(multiply(X3,X2),multiply(X1,X2))) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t220,t298]) ).
cnf(t6417,plain,
add(multiply(X3,X2),multiply(X1,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t6416,t262]) ).
cnf(t371,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X3,X1),X2),
inference(orient,[status(thm)],[t6417]) ).
cnf(t6426,plain,
multiply(add(a,additive_identity),b) = c,
inference(step,[status(thm)],[t64,t371]) ).
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(t6427,plain,
multiply(a,b) = c,
inference(step,[status(thm)],[t6426,t257]) ).
cnf(t418,plain,
multiply(a,b) = c,
inference(orient,[status(thm)],[t6427]) ).
cnf(t419,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(cp,[status(thm)],[t410,t418]) ).
cnf(t1699,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(orient,[status(thm)],[t419]) ).
cnf(t1715,plain,
multiply(b,a) = multiply(b,multiply(c,a)),
inference(cp,[status(thm)],[t425,t1699]) ).
cnf(t1757,plain,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(orient,[status(thm)],[t1715]) ).
cnf(t4,plain,
multiply(X1,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi2,hi17]) ).
cnf(t263,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t374,plain,
multiply(add(X1,X2),X2) = add(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t371,t263]) ).
cnf(t1945,plain,
add(X1,multiply(X2,X1)) = multiply(add(X2,X1),X1),
inference(orient,[status(thm)],[t374]) ).
cnf(t412,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t410,t263]) ).
cnf(t1666,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t412]) ).
cnf(t1677,plain,
multiply(X1,add(multiply(X1,X2),X3)) = add(multiply(X1,X3),multiply(X1,X2)),
inference(cp,[status(thm)],[t383,t1666]) ).
cnf(t6555,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t1677,t383]) ).
cnf(t3563,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t6555]) ).
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(t24,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(t6415,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t24,t262]) ).
cnf(t361,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t6415]) ).
cnf(t3570,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = multiply(X1,additive_identity),
inference(cp,[status(thm)],[t3563,t361]) ).
cnf(t111,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t324,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t111]) ).
cnf(t363,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t324,t361]) ).
cnf(t6476,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t363,t262]) ).
cnf(t1764,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t6476]) ).
cnf(t57,plain,
add(multiply(X1,X1),multiply(X1,additive_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi17,h14]) ).
cnf(t258,plain,
add(multiply(X1,X1),multiply(X1,additive_identity)) = X1,
inference(orient,[status(thm)],[t57]) ).
cnf(t6411,plain,
add(X1,multiply(X1,additive_identity)) = X1,
inference(step,[status(thm)],[t258,t263]) ).
cnf(t264,plain,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[t6411]) ).
cnf(t1621,plain,
add(X1,multiply(X1,additive_identity)) = X1,
inference(orient,[status(thm)],[t264]) ).
cnf(t1766,plain,
multiply(additive_inverse(X1),additive_identity) = add(X1,additive_inverse(X1)),
inference(cp,[status(thm)],[t1764,t1621]) ).
cnf(t6478,plain,
multiply(additive_inverse(X1),additive_identity) = additive_identity,
inference(step,[status(thm)],[t1766,t361]) ).
cnf(t1786,plain,
multiply(additive_inverse(X1),additive_identity) = additive_identity,
inference(orient,[status(thm)],[t6478]) ).
cnf(t1768,plain,
additive_inverse(additive_inverse(X1)) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1764,t361]) ).
cnf(t6477,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t1768,t257]) ).
cnf(t1783,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t6477]) ).
cnf(t1787,plain,
additive_identity = multiply(X1,additive_identity),
inference(cp,[status(thm)],[t1786,t1783]) ).
cnf(t1792,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t1787]) ).
cnf(t6559,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(step,[status(thm)],[t3570,t1792]) ).
cnf(t3681,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t6559]) ).
cnf(t386,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t383,t263]) ).
cnf(t2061,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,X1)),
inference(orient,[status(thm)],[t386]) ).
cnf(t1700,plain,
multiply(c,b) = multiply(a,b),
inference(cp,[status(thm)],[t1699,t263]) ).
cnf(t6473,plain,
multiply(c,b) = c,
inference(step,[status(thm)],[t1700,t418]) ).
cnf(t1716,plain,
multiply(c,b) = c,
inference(orient,[status(thm)],[t6473]) ).
cnf(t1952,plain,
multiply(add(c,b),b) = add(b,c),
inference(cp,[status(thm)],[t1945,t1716]) ).
cnf(t15,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h17]) ).
cnf(t273,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t6483,plain,
multiply(add(c,b),b) = add(c,b),
inference(step,[status(thm)],[t1952,t273]) ).
cnf(t2003,plain,
multiply(add(c,b),b) = add(c,b),
inference(orient,[status(thm)],[t6483]) ).
cnf(t3691,plain,
additive_identity = multiply(add(c,b),add(b,additive_inverse(add(c,b)))),
inference(cp,[status(thm)],[t3681,t2003]) ).
cnf(t71,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t339,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t71]) ).
cnf(t1769,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = add(X2,additive_identity),
inference(cp,[status(thm)],[t1764,t339]) ).
cnf(t6517,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(step,[status(thm)],[t1769,t257]) ).
cnf(t2418,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t6517]) ).
cnf(t2425,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t2418,t1783]) ).
cnf(t2444,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t2425]) ).
cnf(t6560,plain,
additive_identity = multiply(add(c,b),additive_inverse(c)),
inference(step,[status(thm)],[t3691,t2444]) ).
cnf(t3722,plain,
multiply(add(c,b),additive_inverse(c)) = additive_identity,
inference(orient,[status(thm)],[t6560]) ).
cnf(t3726,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t410,t3722]) ).
cnf(t63,plain,
add(multiply(additive_identity,X1),multiply(X1,X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi17,h11]) ).
cnf(t261,plain,
add(multiply(additive_identity,X1),multiply(X1,X1)) = X1,
inference(orient,[status(thm)],[t63]) ).
cnf(t6412,plain,
add(multiply(additive_identity,X1),X1) = X1,
inference(step,[status(thm)],[t261,t263]) ).
cnf(t265,plain,
add(multiply(additive_identity,X1),X1) = X1,
inference(rw,[status(thm)],[t6412]) ).
cnf(t6470,plain,
add(X1,multiply(additive_identity,X1)) = X1,
inference(step,[status(thm)],[t265,t273]) ).
cnf(t1638,plain,
add(X1,multiply(additive_identity,X1)) = X1,
inference(orient,[status(thm)],[t6470]) ).
cnf(t1767,plain,
multiply(additive_identity,additive_inverse(X1)) = add(X1,additive_inverse(X1)),
inference(cp,[status(thm)],[t1764,t1638]) ).
cnf(t6479,plain,
multiply(additive_identity,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t1767,t361]) ).
cnf(t1797,plain,
multiply(additive_identity,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t6479]) ).
cnf(t1798,plain,
additive_identity = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t1797,t1783]) ).
cnf(t1803,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t1798]) ).
cnf(t6582,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = additive_identity,
inference(step,[status(thm)],[t3726,t1803]) ).
cnf(t4029,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = additive_identity,
inference(orient,[status(thm)],[t6582]) ).
cnf(t4042,plain,
multiply(additive_inverse(c),add(c,b)) = multiply(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t425,t4029]) ).
cnf(t6583,plain,
multiply(additive_inverse(c),add(c,b)) = additive_identity,
inference(step,[status(thm)],[t4042,t1786]) ).
cnf(t4043,plain,
multiply(additive_inverse(c),add(c,b)) = additive_identity,
inference(orient,[status(thm)],[t6583]) ).
cnf(t4044,plain,
multiply(additive_inverse(c),add(add(c,b),additive_inverse(c))) = add(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t2061,t4043]) ).
cnf(t6584,plain,
multiply(additive_inverse(c),add(c,add(b,additive_inverse(c)))) = add(additive_inverse(c),additive_identity),
inference(step,[status(thm)],[t4044,t324]) ).
cnf(t1770,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t1764,t273]) ).
cnf(t1926,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t1770]) ).
cnf(t6585,plain,
multiply(additive_inverse(c),b) = add(additive_inverse(c),additive_identity),
inference(step,[status(thm)],[t6584,t1926]) ).
cnf(t6586,plain,
multiply(additive_inverse(c),b) = additive_inverse(c),
inference(step,[status(thm)],[t6585,t257]) ).
cnf(t4054,plain,
multiply(additive_inverse(c),b) = additive_inverse(c),
inference(orient,[status(thm)],[t6586]) ).
cnf(t4057,plain,
multiply(add(additive_inverse(c),b),b) = add(b,additive_inverse(c)),
inference(cp,[status(thm)],[t1945,t4054]) ).
cnf(t6587,plain,
multiply(add(b,additive_inverse(c)),b) = add(b,additive_inverse(c)),
inference(step,[status(thm)],[t4057,t273]) ).
cnf(t4115,plain,
multiply(add(b,additive_inverse(c)),b) = add(b,additive_inverse(c)),
inference(orient,[status(thm)],[t6587]) ).
cnf(t4129,plain,
additive_identity = multiply(add(b,additive_inverse(c)),add(b,additive_inverse(add(b,additive_inverse(c))))),
inference(cp,[status(thm)],[t3681,t4115]) ).
cnf(t2453,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X2,X1))),
inference(cp,[status(thm)],[t2444,t273]) ).
cnf(t2518,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(orient,[status(thm)],[t2453]) ).
cnf(t6588,plain,
additive_identity = multiply(add(b,additive_inverse(c)),additive_inverse(additive_inverse(c))),
inference(step,[status(thm)],[t4129,t2518]) ).
cnf(t6589,plain,
additive_identity = multiply(add(b,additive_inverse(c)),c),
inference(step,[status(thm)],[t6588,t1783]) ).
cnf(t4131,plain,
multiply(add(b,additive_inverse(c)),c) = additive_identity,
inference(orient,[status(thm)],[t6589]) ).
cnf(t4132,plain,
multiply(add(add(b,additive_inverse(c)),c),c) = add(c,additive_identity),
inference(cp,[status(thm)],[t1945,t4131]) ).
cnf(t6596,plain,
multiply(add(b,add(additive_inverse(c),c)),c) = add(c,additive_identity),
inference(step,[status(thm)],[t4132,t324]) ).
cnf(t6597,plain,
multiply(add(c,add(b,additive_inverse(c))),c) = add(c,additive_identity),
inference(step,[status(thm)],[t6596,t298]) ).
cnf(t6598,plain,
multiply(b,c) = add(c,additive_identity),
inference(step,[status(thm)],[t6597,t1926]) ).
cnf(t6599,plain,
multiply(b,c) = c,
inference(step,[status(thm)],[t6598,t257]) ).
cnf(t4289,plain,
multiply(b,c) = c,
inference(orient,[status(thm)],[t6599]) ).
cnf(t4295,plain,
multiply(b,multiply(c,X1)) = multiply(c,X1),
inference(cp,[status(thm)],[t410,t4289]) ).
cnf(t4351,plain,
multiply(b,multiply(c,X1)) = multiply(c,X1),
inference(orient,[status(thm)],[t4295]) ).
cnf(t6603,plain,
multiply(c,a) = multiply(b,a),
inference(step,[status(thm)],[t1757,t4351]) ).
cnf(t4362,plain,
multiply(c,a) = multiply(b,a),
inference(rw,[status(thm)],[t6603]) ).
cnf(t4363,plain,
multiply(b,a) = multiply(c,a),
inference(orient,[status(thm)],[t4362]) ).
cnf(t4368,plain,
true = product(b,a,multiply(c,a)),
inference(cp,[status(thm)],[t476,t4363]) ).
cnf(t4880,plain,
product(b,a,multiply(c,a)) = true,
inference(orient,[status(thm)],[t4368]) ).
cnf(t1668,plain,
multiply(a,b) = multiply(a,c),
inference(cp,[status(thm)],[t1666,t418]) ).
cnf(t6472,plain,
c = multiply(a,c),
inference(step,[status(thm)],[t1668,t418]) ).
cnf(t1687,plain,
multiply(a,c) = c,
inference(orient,[status(thm)],[t6472]) ).
cnf(t1692,plain,
multiply(add(a,X1),c) = add(multiply(X1,c),c),
inference(cp,[status(thm)],[t371,t1687]) ).
cnf(t6501,plain,
multiply(add(a,X1),c) = add(c,multiply(X1,c)),
inference(step,[status(thm)],[t1692,t273]) ).
cnf(t6502,plain,
multiply(add(a,X1),c) = multiply(add(X1,c),c),
inference(step,[status(thm)],[t6501,t1945]) ).
cnf(t2267,plain,
multiply(add(a,X1),c) = multiply(add(X1,c),c),
inference(orient,[status(thm)],[t6502]) ).
cnf(t2280,plain,
multiply(add(a,X1),c) = multiply(add(c,X1),c),
inference(cp,[status(thm)],[t2267,t273]) ).
cnf(t2359,plain,
multiply(add(a,X1),c) = multiply(add(c,X1),c),
inference(orient,[status(thm)],[t2280]) ).
cnf(t2362,plain,
multiply(add(c,additive_inverse(a)),c) = multiply(additive_identity,c),
inference(cp,[status(thm)],[t2359,t361]) ).
cnf(t6514,plain,
multiply(add(c,additive_inverse(a)),c) = additive_identity,
inference(step,[status(thm)],[t2362,t1803]) ).
cnf(t2379,plain,
multiply(add(c,additive_inverse(a)),c) = additive_identity,
inference(orient,[status(thm)],[t6514]) ).
cnf(t2384,plain,
multiply(add(c,additive_inverse(a)),multiply(c,X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t410,t2379]) ).
cnf(t6538,plain,
multiply(add(c,additive_inverse(a)),multiply(c,X1)) = additive_identity,
inference(step,[status(thm)],[t2384,t1803]) ).
cnf(t3190,plain,
multiply(add(c,additive_inverse(a)),multiply(c,X1)) = additive_identity,
inference(orient,[status(thm)],[t6538]) ).
cnf(t3200,plain,
multiply(c,add(c,additive_inverse(a))) = multiply(c,additive_identity),
inference(cp,[status(thm)],[t425,t3190]) ).
cnf(t6539,plain,
multiply(c,add(c,additive_inverse(a))) = additive_identity,
inference(step,[status(thm)],[t3200,t1792]) ).
cnf(t3201,plain,
multiply(c,add(c,additive_inverse(a))) = additive_identity,
inference(orient,[status(thm)],[t6539]) ).
cnf(t3203,plain,
multiply(c,add(add(c,additive_inverse(a)),c)) = add(c,additive_identity),
inference(cp,[status(thm)],[t2061,t3201]) ).
cnf(t6545,plain,
multiply(c,add(c,add(additive_inverse(a),c))) = add(c,additive_identity),
inference(step,[status(thm)],[t3203,t324]) ).
cnf(t6546,plain,
multiply(c,add(c,add(c,additive_inverse(a)))) = add(c,additive_identity),
inference(step,[status(thm)],[t6545,t298]) ).
cnf(t6547,plain,
multiply(c,add(c,add(c,additive_inverse(a)))) = c,
inference(step,[status(thm)],[t6546,t257]) ).
cnf(t3432,plain,
multiply(c,add(c,add(c,additive_inverse(a)))) = c,
inference(orient,[status(thm)],[t6547]) ).
cnf(t4047,plain,
multiply(additive_inverse(c),multiply(add(c,b),X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t410,t4043]) ).
cnf(t6595,plain,
multiply(additive_inverse(c),multiply(add(c,b),X1)) = additive_identity,
inference(step,[status(thm)],[t4047,t1803]) ).
cnf(t4276,plain,
multiply(additive_inverse(c),multiply(add(c,b),X1)) = additive_identity,
inference(orient,[status(thm)],[t6595]) ).
cnf(t4292,plain,
multiply(add(b,c),c) = add(c,c),
inference(cp,[status(thm)],[t1945,t4289]) ).
cnf(t6602,plain,
multiply(add(c,b),c) = add(c,c),
inference(step,[status(thm)],[t4292,t273]) ).
cnf(t4334,plain,
multiply(add(c,b),c) = add(c,c),
inference(orient,[status(thm)],[t6602]) ).
cnf(t4347,plain,
additive_identity = multiply(additive_inverse(c),add(c,c)),
inference(cp,[status(thm)],[t4276,t4334]) ).
cnf(t4388,plain,
multiply(additive_inverse(c),add(c,c)) = additive_identity,
inference(orient,[status(thm)],[t4347]) ).
cnf(t4389,plain,
multiply(additive_inverse(c),add(add(c,c),additive_inverse(c))) = add(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t2061,t4388]) ).
cnf(t6606,plain,
multiply(additive_inverse(c),add(c,add(c,additive_inverse(c)))) = add(additive_inverse(c),additive_identity),
inference(step,[status(thm)],[t4389,t324]) ).
cnf(t6607,plain,
multiply(additive_inverse(c),c) = add(additive_inverse(c),additive_identity),
inference(step,[status(thm)],[t6606,t1926]) ).
cnf(t6608,plain,
multiply(additive_inverse(c),c) = additive_inverse(c),
inference(step,[status(thm)],[t6607,t257]) ).
cnf(t4399,plain,
multiply(additive_inverse(c),c) = additive_inverse(c),
inference(orient,[status(thm)],[t6608]) ).
cnf(t4400,plain,
multiply(additive_inverse(c),add(c,additive_inverse(c))) = add(additive_inverse(c),additive_inverse(c)),
inference(cp,[status(thm)],[t2061,t4399]) ).
cnf(t6609,plain,
multiply(additive_inverse(c),additive_identity) = add(additive_inverse(c),additive_inverse(c)),
inference(step,[status(thm)],[t4400,t361]) ).
cnf(t6610,plain,
additive_identity = add(additive_inverse(c),additive_inverse(c)),
inference(step,[status(thm)],[t6609,t1786]) ).
cnf(t2462,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(cp,[status(thm)],[t1764,t2444]) ).
cnf(t2471,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(orient,[status(thm)],[t2462]) ).
cnf(t2474,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(cp,[status(thm)],[t2471,t1783]) ).
cnf(t2498,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(orient,[status(thm)],[t2474]) ).
cnf(t6611,plain,
additive_identity = additive_inverse(add(c,c)),
inference(step,[status(thm)],[t6610,t2498]) ).
cnf(t4412,plain,
additive_inverse(add(c,c)) = additive_identity,
inference(orient,[status(thm)],[t6611]) ).
cnf(t4436,plain,
additive_inverse(c) = add(c,additive_identity),
inference(cp,[status(thm)],[t2518,t4412]) ).
cnf(t6612,plain,
additive_inverse(c) = c,
inference(step,[status(thm)],[t4436,t257]) ).
cnf(t4442,plain,
additive_inverse(c) = c,
inference(orient,[status(thm)],[t6612]) ).
cnf(t4463,plain,
X1 = add(c,add(c,X1)),
inference(cp,[status(thm)],[t1764,t4442]) ).
cnf(t4528,plain,
add(c,add(c,X1)) = X1,
inference(orient,[status(thm)],[t4463]) ).
cnf(t6642,plain,
multiply(c,additive_inverse(a)) = c,
inference(step,[status(thm)],[t3432,t4528]) ).
cnf(t4550,plain,
multiply(c,additive_inverse(a)) = c,
inference(rw,[status(thm)],[t6642]) ).
cnf(t4578,plain,
multiply(c,additive_inverse(a)) = c,
inference(orient,[status(thm)],[t4550]) ).
cnf(t4585,plain,
multiply(c,add(X1,additive_inverse(a))) = add(c,multiply(c,X1)),
inference(cp,[status(thm)],[t383,t4578]) ).
cnf(t6688,plain,
multiply(c,add(X1,additive_inverse(a))) = multiply(c,add(X1,c)),
inference(step,[status(thm)],[t4585,t2061]) ).
cnf(t6306,plain,
multiply(c,add(X1,additive_inverse(a))) = multiply(c,add(X1,c)),
inference(orient,[status(thm)],[t6688]) ).
cnf(t6309,plain,
multiply(c,add(a,c)) = multiply(c,additive_identity),
inference(cp,[status(thm)],[t6306,t361]) ).
cnf(t6689,plain,
multiply(c,add(c,a)) = multiply(c,additive_identity),
inference(step,[status(thm)],[t6309,t273]) ).
cnf(t6690,plain,
multiply(c,add(c,a)) = additive_identity,
inference(step,[status(thm)],[t6689,t1792]) ).
cnf(t6330,plain,
multiply(c,add(c,a)) = additive_identity,
inference(orient,[status(thm)],[t6690]) ).
cnf(t6333,plain,
multiply(c,add(add(c,a),c)) = add(c,additive_identity),
inference(cp,[status(thm)],[t2061,t6330]) ).
cnf(t6693,plain,
multiply(c,add(c,add(a,c))) = add(c,additive_identity),
inference(step,[status(thm)],[t6333,t324]) ).
cnf(t4462,plain,
X1 = add(c,add(X1,c)),
inference(cp,[status(thm)],[t1926,t4442]) ).
cnf(t4511,plain,
add(c,add(X1,c)) = X1,
inference(orient,[status(thm)],[t4462]) ).
cnf(t6694,plain,
multiply(c,a) = add(c,additive_identity),
inference(step,[status(thm)],[t6693,t4511]) ).
cnf(t6695,plain,
multiply(c,a) = c,
inference(step,[status(thm)],[t6694,t257]) ).
cnf(t6344,plain,
multiply(c,a) = c,
inference(orient,[status(thm)],[t6695]) ).
cnf(t6702,plain,
product(b,a,c) = true,
inference(step,[status(thm)],[t4880,t6344]) ).
cnf(t6364,plain,
product(b,a,c) = true,
inference(rw,[status(thm)],[t6702]) ).
cnf(t6388,plain,
product(b,a,c) = true,
inference(orient,[status(thm)],[t6364]) ).
cnf(f19,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f19_nnf,plain,
~ product(b,a,c),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ product(b,a,c),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
product(b,a,c) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6388]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:45:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 35.84/5.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.84/5.32 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------