%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO014-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 12:59:36 PM UTC 2026
% Result : Unsatisfiable 52.74s 22.91s
% Output : Proof 52.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 22
% Syntax : Number of formulae : 309 ( 269 unt; 0 def)
% Number of atoms : 441 ( 234 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 271 ( 139 ~; 132 |; 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 : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 605 ( 20 sgn 142 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,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(f10_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)],[f10]) ).
fof(f10_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)],[f10_nnf]) ).
cnf(c10,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)],[f10_sk]) ).
cnf(hi10,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)],[c10]) ).
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(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(h24,plain,
sum(multiply(V0,V1),multiply(V2,V1),multiply(add(V0,V2),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi1,hi1,hi0,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(t188,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X3,X1),X2),
inference(hyper_resolution,[status(thm)],[hi20,h1,h24]) ).
cnf(t445,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X3,X1),X2),
inference(orient,[status(thm)],[t188]) ).
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(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(t12,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi19]) ).
cnf(t327,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t12]) ).
cnf(t449,plain,
multiply(add(X1,X2),inverse(X2)) = add(additive_identity,multiply(X1,inverse(X2))),
inference(cp,[status(thm)],[t445,t327]) ).
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(t243,plain,
multiply(add(multiply(X1,X2),X3),add(multiply(X1,X2),X2)) = multiply(add(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi20,h13,h24]) ).
cnf(t413,plain,
multiply(add(multiply(X1,X2),X3),add(multiply(X1,X2),X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t243]) ).
cnf(t424,plain,
multiply(add(X1,X2),inverse(X1)) = multiply(add(additive_identity,X2),add(multiply(X1,inverse(X1)),inverse(X1))),
inference(cp,[status(thm)],[t413,t327]) ).
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(t3,plain,
add(additive_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi20,hi4,hi0]) ).
cnf(t265,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t5472,plain,
multiply(add(X1,X2),inverse(X1)) = multiply(X2,add(multiply(X1,inverse(X1)),inverse(X1))),
inference(step,[status(thm)],[t424,t265]) ).
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(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(t200,plain,
multiply(add(X1,X2),add(X3,X2)) = add(multiply(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h5]) ).
cnf(t199,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(hyper_resolution,[status(thm)],[hi20,h1,h5]) ).
cnf(t524,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(orient,[status(thm)],[t199]) ).
cnf(t5356,plain,
add(X2,multiply(X1,X3)) = add(multiply(X1,X3),X2),
inference(step,[status(thm)],[t200,t524]) ).
cnf(t553,plain,
add(X1,multiply(X2,X3)) = add(multiply(X2,X3),X1),
inference(orient,[status(thm)],[t5356]) ).
cnf(t5473,plain,
multiply(add(X1,X2),inverse(X1)) = multiply(X2,add(inverse(X1),multiply(X1,inverse(X1)))),
inference(step,[status(thm)],[t5472,t553]) ).
cnf(f12,axiom,
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity5) ).
fof(f12_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X3,X4),true,ifeq(product(X1,X3,X5),true,ifeq(sum(X0,X5,X6),true,product(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h20,plain,
product(add(V0,V1),add(V0,V2),add(V0,multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi0,hi0,hi1,hi0]) ).
cnf(f14,axiom,
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity7) ).
fof(f14_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X2,X4,X6)
| ~ sum(X5,X1,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(product(X0,X3,X5),true,ifeq(sum(X5,X1,X6),true,product(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h7,plain,
product(V0,add(V1,V0),add(multiply(additive_identity,V1),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi4,hi0,hi1,hi0]) ).
cnf(t227,plain,
add(multiply(additive_identity,X1),add(X1,X2)) = add(X1,multiply(X2,add(X1,X2))),
inference(hyper_resolution,[status(thm)],[hi21,h7,h20]) ).
cnf(t703,plain,
add(X1,multiply(X2,add(X1,X2))) = add(multiply(additive_identity,X1),add(X1,X2)),
inference(orient,[status(thm)],[t227]) ).
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(hi9,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)],[c9]) ).
cnf(h25,plain,
product(V0,V1,add(multiply(V0,additive_identity),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi1,hi1,hi4,hi0]) ).
cnf(t101,plain,
add(multiply(X1,additive_identity),multiply(X1,X2)) = multiply(X1,X2),
inference(hyper_resolution,[status(thm)],[hi21,hi1,h25]) ).
cnf(t286,plain,
add(multiply(X1,additive_identity),multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t101]) ).
cnf(t330,plain,
multiply(X1,inverse(X1)) = add(multiply(X1,additive_identity),additive_identity),
inference(cp,[status(thm)],[t286,t327]) ).
cnf(t5393,plain,
additive_identity = add(multiply(X1,additive_identity),additive_identity),
inference(step,[status(thm)],[t330,t327]) ).
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(t5394,plain,
additive_identity = multiply(X1,additive_identity),
inference(step,[status(thm)],[t5393,t258]) ).
cnf(t2114,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t5394]) ).
cnf(t2116,plain,
add(additive_identity,multiply(X1,add(additive_identity,X1))) = add(additive_identity,add(additive_identity,X1)),
inference(cp,[status(thm)],[t703,t2114]) ).
cnf(t5411,plain,
multiply(X1,add(additive_identity,X1)) = add(additive_identity,add(additive_identity,X1)),
inference(step,[status(thm)],[t2116,t265]) ).
cnf(t5412,plain,
multiply(X1,X1) = add(additive_identity,add(additive_identity,X1)),
inference(step,[status(thm)],[t5411,t265]) ).
cnf(t5413,plain,
multiply(X1,X1) = add(additive_identity,X1),
inference(step,[status(thm)],[t5412,t265]) ).
cnf(t5414,plain,
multiply(X1,X1) = X1,
inference(step,[status(thm)],[t5413,t265]) ).
cnf(t2128,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t5414]) ).
cnf(t2130,plain,
multiply(add(X1,X2),X2) = add(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t445,t2128]) ).
cnf(h4,plain,
sum(multiply(V0,additive_identity),V1,multiply(add(V0,V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi0,hi4,hi1,hi1]) ).
cnf(t111,plain,
multiply(add(X1,X2),X2) = add(multiply(X1,additive_identity),X2),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h4]) ).
cnf(t504,plain,
add(multiply(X1,additive_identity),X2) = multiply(add(X1,X2),X2),
inference(orient,[status(thm)],[t111]) ).
cnf(t5405,plain,
add(additive_identity,X2) = multiply(add(X1,X2),X2),
inference(step,[status(thm)],[t504,t2114]) ).
cnf(t5406,plain,
X2 = multiply(add(X1,X2),X2),
inference(step,[status(thm)],[t5405,t265]) ).
cnf(t2125,plain,
X2 = multiply(add(X1,X2),X2),
inference(rw,[status(thm)],[t5406]) ).
cnf(t2268,plain,
multiply(add(X1,X2),X2) = X2,
inference(orient,[status(thm)],[t2125]) ).
cnf(t5423,plain,
X2 = add(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t2130,t2268]) ).
cnf(t2524,plain,
add(X1,multiply(X2,X1)) = X1,
inference(orient,[status(thm)],[t5423]) ).
cnf(t5474,plain,
multiply(add(X1,X2),inverse(X1)) = multiply(X2,inverse(X1)),
inference(step,[status(thm)],[t5473,t2524]) ).
cnf(t3457,plain,
multiply(add(X1,X2),inverse(X1)) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t5474]) ).
cnf(t197,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h13]) ).
cnf(t573,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t197]) ).
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(t10,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi17]) ).
cnf(t771,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t10]) ).
cnf(t775,plain,
add(X1,multiply(inverse(X1),X2)) = multiply(multiplicative_identity,add(X1,X2)),
inference(cp,[status(thm)],[t573,t771]) ).
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(t8,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)],[t8]) ).
cnf(t5449,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(step,[status(thm)],[t775,t257]) ).
cnf(t3146,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(orient,[status(thm)],[t5449]) ).
cnf(t3458,plain,
multiply(multiply(inverse(X1),X2),inverse(X1)) = multiply(add(X1,X2),inverse(X1)),
inference(cp,[status(thm)],[t3457,t3146]) ).
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(t107,plain,
multiply(X1,add(X2,X1)) = add(multiply(additive_identity,X2),X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h3]) ).
cnf(t313,plain,
add(multiply(additive_identity,X1),X2) = multiply(X2,add(X1,X2)),
inference(orient,[status(thm)],[t107]) ).
cnf(t2546,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(multiply(X2,X1),X1),
inference(cp,[status(thm)],[t313,t2524]) ).
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(t103,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(hyper_resolution,[status(thm)],[hi21,hi1,h21]) ).
cnf(t290,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(orient,[status(thm)],[t103]) ).
cnf(t5425,plain,
multiply(X2,X1) = multiply(multiply(X2,X1),X1),
inference(step,[status(thm)],[t2546,t290]) ).
cnf(t2600,plain,
multiply(multiply(X1,X2),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t5425]) ).
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(t13,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi18]) ).
cnf(t623,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(orient,[status(thm)],[t13]) ).
cnf(t2601,plain,
multiply(inverse(X1),X1) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t2600,t623]) ).
cnf(t5426,plain,
additive_identity = multiply(additive_identity,X1),
inference(step,[status(thm)],[t2601,t623]) ).
cnf(t2607,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t5426]) ).
cnf(t5429,plain,
add(additive_identity,X2) = multiply(X2,add(X1,X2)),
inference(step,[status(thm)],[t313,t2607]) ).
cnf(t5430,plain,
X2 = multiply(X2,add(X1,X2)),
inference(step,[status(thm)],[t5429,t265]) ).
cnf(t2609,plain,
X2 = multiply(X2,add(X1,X2)),
inference(rw,[status(thm)],[t5430]) ).
cnf(t2616,plain,
multiply(X1,add(X2,X1)) = X1,
inference(orient,[status(thm)],[t2609]) ).
cnf(t2525,plain,
X1 = add(X1,X1),
inference(cp,[status(thm)],[t2524,t2128]) ).
cnf(t2548,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t2525]) ).
cnf(t2549,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,X1)),
inference(cp,[status(thm)],[t524,t2548]) ).
cnf(t5442,plain,
add(X1,multiply(X1,X2)) = X1,
inference(step,[status(thm)],[t2549,t2616]) ).
cnf(t3009,plain,
add(X1,multiply(X1,X2)) = X1,
inference(orient,[status(thm)],[t5442]) ).
cnf(t3020,plain,
multiply(X1,X2) = multiply(multiply(X1,X2),X1),
inference(cp,[status(thm)],[t2616,t3009]) ).
cnf(t3318,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,X2),
inference(orient,[status(thm)],[t3020]) ).
cnf(t5479,plain,
multiply(inverse(X1),X2) = multiply(add(X1,X2),inverse(X1)),
inference(step,[status(thm)],[t3458,t3318]) ).
cnf(t5480,plain,
multiply(inverse(X1),X2) = multiply(X2,inverse(X1)),
inference(step,[status(thm)],[t5479,t3457]) ).
cnf(t3494,plain,
multiply(inverse(X1),X2) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t5480]) ).
cnf(t5494,plain,
multiply(inverse(X2),add(X1,X2)) = add(additive_identity,multiply(X1,inverse(X2))),
inference(step,[status(thm)],[t449,t3494]) ).
cnf(t5495,plain,
multiply(inverse(X2),add(X1,X2)) = multiply(X1,inverse(X2)),
inference(step,[status(thm)],[t5494,t265]) ).
cnf(t3626,plain,
multiply(inverse(X1),add(X2,X1)) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t5495]) ).
cnf(h22,plain,
product(add(V0,V1),V2,add(multiply(V0,V2),multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi1,hi1,hi0,hi0]) ).
cnf(h9,plain,
product(add(V0,V1),add(V2,V1),add(multiply(V0,V2),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi0,hi0,hi1,hi0]) ).
cnf(t236,plain,
add(multiply(X1,add(X2,X3)),multiply(X3,add(X2,X3))) = add(multiply(X1,X2),X3),
inference(hyper_resolution,[status(thm)],[hi21,h9,h22]) ).
cnf(t5359,plain,
multiply(add(X3,X1),add(X2,X3)) = add(multiply(X1,X2),X3),
inference(step,[status(thm)],[t236,t445]) ).
cnf(t785,plain,
multiply(add(X1,X2),add(X3,X1)) = add(multiply(X2,X3),X1),
inference(orient,[status(thm)],[t5359]) ).
cnf(t773,plain,
add(inverse(X1),multiply(X1,X2)) = multiply(multiplicative_identity,add(X2,inverse(X1))),
inference(cp,[status(thm)],[t524,t771]) ).
cnf(t5496,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(step,[status(thm)],[t773,t257]) ).
cnf(t3651,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(orient,[status(thm)],[t5496]) ).
cnf(t581,plain,
add(X1,multiply(additive_identity,X2)) = multiply(X1,add(X1,X2)),
inference(cp,[status(thm)],[t573,t258]) ).
cnf(t5434,plain,
add(X1,additive_identity) = multiply(X1,add(X1,X2)),
inference(step,[status(thm)],[t581,t2607]) ).
cnf(t5435,plain,
X1 = multiply(X1,add(X1,X2)),
inference(step,[status(thm)],[t5434,t258]) ).
cnf(t2637,plain,
multiply(X1,add(X1,X2)) = X1,
inference(orient,[status(thm)],[t5435]) ).
cnf(f22,negated_conjecture,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
fof(f22_nnf,plain,
sum(x,y,x_plus_y),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
sum(x,y,x_plus_y),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,negated_conjecture,
sum(x,y,x_plus_y) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t5,plain,
add(x,y) = x_plus_y,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi22]) ).
cnf(t19,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h1]) ).
cnf(t642,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t19]) ).
cnf(t5361,plain,
add(y,x) = x_plus_y,
inference(step,[status(thm)],[t5,t642]) ).
cnf(t891,plain,
add(y,x) = x_plus_y,
inference(orient,[status(thm)],[t5361]) ).
cnf(t2638,plain,
y = multiply(y,x_plus_y),
inference(cp,[status(thm)],[t2637,t891]) ).
cnf(t2645,plain,
multiply(y,x_plus_y) = y,
inference(orient,[status(thm)],[t2638]) ).
cnf(t3654,plain,
add(x_plus_y,inverse(y)) = add(inverse(y),y),
inference(cp,[status(thm)],[t3651,t2645]) ).
cnf(t5497,plain,
add(x_plus_y,inverse(y)) = add(y,inverse(y)),
inference(step,[status(thm)],[t3654,t642]) ).
cnf(t5498,plain,
add(x_plus_y,inverse(y)) = multiplicative_identity,
inference(step,[status(thm)],[t5497,t771]) ).
cnf(t3680,plain,
add(x_plus_y,inverse(y)) = multiplicative_identity,
inference(orient,[status(thm)],[t5498]) ).
cnf(t3686,plain,
add(multiply(inverse(y),X1),x_plus_y) = multiply(multiplicative_identity,add(X1,x_plus_y)),
inference(cp,[status(thm)],[t785,t3680]) ).
cnf(t5597,plain,
add(x_plus_y,multiply(inverse(y),X1)) = multiply(multiplicative_identity,add(X1,x_plus_y)),
inference(step,[status(thm)],[t3686,t553]) ).
cnf(t5598,plain,
add(x_plus_y,multiply(inverse(y),X1)) = add(X1,x_plus_y),
inference(step,[status(thm)],[t5597,t257]) ).
cnf(t5273,plain,
add(x_plus_y,multiply(inverse(y),X1)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t5598]) ).
cnf(f23,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
fof(f23_nnf,plain,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,negated_conjecture,
product(inverse(x),inverse(y),x_inverse_times_y_inverse) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t25,plain,
multiply(inverse(x),inverse(y)) = x_inverse_times_y_inverse,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi23]) ).
cnf(t634,plain,
multiply(inverse(x),inverse(y)) = x_inverse_times_y_inverse,
inference(orient,[status(thm)],[t25]) ).
cnf(t3148,plain,
add(x,inverse(y)) = add(x,x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t3146,t634]) ).
cnf(t5450,plain,
add(x,inverse(y)) = add(x_inverse_times_y_inverse,x),
inference(step,[status(thm)],[t3148,t642]) ).
cnf(t3165,plain,
add(x,inverse(y)) = add(x_inverse_times_y_inverse,x),
inference(orient,[status(thm)],[t5450]) ).
cnf(t3462,plain,
multiply(inverse(y),inverse(x)) = multiply(add(x_inverse_times_y_inverse,x),inverse(x)),
inference(cp,[status(thm)],[t3457,t3165]) ).
cnf(t5574,plain,
multiply(inverse(y),inverse(x)) = multiply(inverse(x),add(x_inverse_times_y_inverse,x)),
inference(step,[status(thm)],[t3462,t3494]) ).
cnf(t5575,plain,
multiply(inverse(y),inverse(x)) = multiply(x_inverse_times_y_inverse,inverse(x)),
inference(step,[status(thm)],[t5574,t3626]) ).
cnf(t3010,plain,
inverse(x) = add(inverse(x),x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t3009,t634]) ).
cnf(t5443,plain,
inverse(x) = add(x_inverse_times_y_inverse,inverse(x)),
inference(step,[status(thm)],[t3010,t642]) ).
cnf(t3028,plain,
add(x_inverse_times_y_inverse,inverse(x)) = inverse(x),
inference(orient,[status(thm)],[t5443]) ).
cnf(t3033,plain,
x_inverse_times_y_inverse = multiply(x_inverse_times_y_inverse,inverse(x)),
inference(cp,[status(thm)],[t2637,t3028]) ).
cnf(t3041,plain,
multiply(x_inverse_times_y_inverse,inverse(x)) = x_inverse_times_y_inverse,
inference(orient,[status(thm)],[t3033]) ).
cnf(t5576,plain,
multiply(inverse(y),inverse(x)) = x_inverse_times_y_inverse,
inference(step,[status(thm)],[t5575,t3041]) ).
cnf(t4871,plain,
multiply(inverse(y),inverse(x)) = x_inverse_times_y_inverse,
inference(orient,[status(thm)],[t5576]) ).
cnf(t5275,plain,
add(inverse(x),x_plus_y) = add(x_plus_y,x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t5273,t4871]) ).
cnf(t5601,plain,
add(x_plus_y,inverse(x)) = add(x_plus_y,x_inverse_times_y_inverse),
inference(step,[status(thm)],[t5275,t642]) ).
cnf(t774,plain,
add(inverse(X1),multiply(X2,X1)) = multiply(add(X2,inverse(X1)),multiplicative_identity),
inference(cp,[status(thm)],[t524,t771]) ).
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(t7,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)],[t7]) ).
cnf(t5502,plain,
add(inverse(X1),multiply(X2,X1)) = add(X2,inverse(X1)),
inference(step,[status(thm)],[t774,t256]) ).
cnf(t3771,plain,
add(inverse(X1),multiply(X2,X1)) = add(X2,inverse(X1)),
inference(orient,[status(thm)],[t5502]) ).
cnf(t2269,plain,
x = multiply(x_plus_y,x),
inference(cp,[status(thm)],[t2268,t891]) ).
cnf(t2277,plain,
multiply(x_plus_y,x) = x,
inference(orient,[status(thm)],[t2269]) ).
cnf(t3779,plain,
add(x_plus_y,inverse(x)) = add(inverse(x),x),
inference(cp,[status(thm)],[t3771,t2277]) ).
cnf(t5503,plain,
add(x_plus_y,inverse(x)) = add(x,inverse(x)),
inference(step,[status(thm)],[t3779,t642]) ).
cnf(t5504,plain,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(step,[status(thm)],[t5503,t771]) ).
cnf(t3796,plain,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(orient,[status(thm)],[t5504]) ).
cnf(t5602,plain,
multiplicative_identity = add(x_plus_y,x_inverse_times_y_inverse),
inference(step,[status(thm)],[t5601,t3796]) ).
cnf(t5316,plain,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(orient,[status(thm)],[t5602]) ).
cnf(t5319,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = multiply(inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(cp,[status(thm)],[t3626,t5316]) ).
cnf(t625,plain,
multiply(add(X1,inverse(X2)),X2) = add(additive_identity,multiply(X1,X2)),
inference(cp,[status(thm)],[t445,t623]) ).
cnf(t5444,plain,
multiply(add(X1,inverse(X2)),X2) = multiply(X1,X2),
inference(step,[status(thm)],[t625,t265]) ).
cnf(t3054,plain,
multiply(add(X1,inverse(X2)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t5444]) ).
cnf(t2529,plain,
inverse(y) = add(inverse(y),x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t2524,t634]) ).
cnf(t5424,plain,
inverse(y) = add(x_inverse_times_y_inverse,inverse(y)),
inference(step,[status(thm)],[t2529,t642]) ).
cnf(t2577,plain,
add(x_inverse_times_y_inverse,inverse(y)) = inverse(y),
inference(orient,[status(thm)],[t5424]) ).
cnf(t3057,plain,
multiply(x_inverse_times_y_inverse,y) = multiply(inverse(y),y),
inference(cp,[status(thm)],[t3054,t2577]) ).
cnf(t5445,plain,
multiply(x_inverse_times_y_inverse,y) = additive_identity,
inference(step,[status(thm)],[t3057,t623]) ).
cnf(t3066,plain,
multiply(x_inverse_times_y_inverse,y) = additive_identity,
inference(orient,[status(thm)],[t5445]) ).
cnf(t3524,plain,
multiply(x_inverse_times_y_inverse,y) = additive_identity,
inference(rw,[status(thm)],[t3066]) ).
cnf(t3151,plain,
add(X1,inverse(inverse(X1))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t3146,t327]) ).
cnf(t5456,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(step,[status(thm)],[t3151,t258]) ).
cnf(t3184,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(orient,[status(thm)],[t5456]) ).
cnf(t3189,plain,
inverse(inverse(X1)) = multiply(inverse(inverse(X1)),X1),
inference(cp,[status(thm)],[t2616,t3184]) ).
cnf(t626,plain,
multiply(add(inverse(X1),X2),X1) = add(multiply(X2,X1),additive_identity),
inference(cp,[status(thm)],[t445,t623]) ).
cnf(t5447,plain,
multiply(add(inverse(X1),X2),X1) = multiply(X2,X1),
inference(step,[status(thm)],[t626,t258]) ).
cnf(t3126,plain,
multiply(add(inverse(X1),X2),X1) = multiply(X2,X1),
inference(orient,[status(thm)],[t5447]) ).
cnf(t3130,plain,
multiply(inverse(inverse(X1)),X1) = multiply(multiplicative_identity,X1),
inference(cp,[status(thm)],[t3126,t771]) ).
cnf(t5448,plain,
multiply(inverse(inverse(X1)),X1) = X1,
inference(step,[status(thm)],[t3130,t257]) ).
cnf(t3138,plain,
multiply(inverse(inverse(X1)),X1) = X1,
inference(orient,[status(thm)],[t5448]) ).
cnf(t5457,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t3189,t3138]) ).
cnf(t3198,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t5457]) ).
cnf(t3495,plain,
multiply(X1,inverse(inverse(X2))) = multiply(X2,X1),
inference(cp,[status(thm)],[t3494,t3198]) ).
cnf(t5481,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(step,[status(thm)],[t3495,t3198]) ).
cnf(t3519,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t5481]) ).
cnf(t5486,plain,
multiply(y,x_inverse_times_y_inverse) = additive_identity,
inference(step,[status(thm)],[t3524,t3519]) ).
cnf(t3534,plain,
multiply(y,x_inverse_times_y_inverse) = additive_identity,
inference(orient,[status(thm)],[t5486]) ).
cnf(t3537,plain,
multiply(add(y,X1),x_inverse_times_y_inverse) = add(multiply(X1,x_inverse_times_y_inverse),additive_identity),
inference(cp,[status(thm)],[t445,t3534]) ).
cnf(t5545,plain,
multiply(x_inverse_times_y_inverse,add(y,X1)) = add(multiply(X1,x_inverse_times_y_inverse),additive_identity),
inference(step,[status(thm)],[t3537,t3519]) ).
cnf(t5546,plain,
multiply(x_inverse_times_y_inverse,add(y,X1)) = multiply(X1,x_inverse_times_y_inverse),
inference(step,[status(thm)],[t5545,t258]) ).
cnf(t4279,plain,
multiply(x_inverse_times_y_inverse,add(y,X1)) = multiply(X1,x_inverse_times_y_inverse),
inference(orient,[status(thm)],[t5546]) ).
cnf(t4283,plain,
multiply(x,x_inverse_times_y_inverse) = multiply(x_inverse_times_y_inverse,x_plus_y),
inference(cp,[status(thm)],[t4279,t891]) ).
cnf(t5547,plain,
multiply(x_inverse_times_y_inverse,x) = multiply(x_inverse_times_y_inverse,x_plus_y),
inference(step,[status(thm)],[t4283,t3519]) ).
cnf(t3058,plain,
multiply(x_inverse_times_y_inverse,x) = multiply(inverse(x),x),
inference(cp,[status(thm)],[t3054,t3028]) ).
cnf(t5446,plain,
multiply(x_inverse_times_y_inverse,x) = additive_identity,
inference(step,[status(thm)],[t3058,t623]) ).
cnf(t3072,plain,
multiply(x_inverse_times_y_inverse,x) = additive_identity,
inference(orient,[status(thm)],[t5446]) ).
cnf(t5548,plain,
additive_identity = multiply(x_inverse_times_y_inverse,x_plus_y),
inference(step,[status(thm)],[t5547,t3072]) ).
cnf(t5549,plain,
additive_identity = multiply(x_plus_y,x_inverse_times_y_inverse),
inference(step,[status(thm)],[t5548,t3519]) ).
cnf(t4301,plain,
multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
inference(orient,[status(thm)],[t5549]) ).
cnf(t4302,plain,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = add(inverse(x_inverse_times_y_inverse),additive_identity),
inference(cp,[status(thm)],[t3771,t4301]) ).
cnf(t5550,plain,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(step,[status(thm)],[t4302,t258]) ).
cnf(t4356,plain,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(orient,[status(thm)],[t5550]) ).
cnf(t4362,plain,
x_plus_y = multiply(x_plus_y,inverse(x_inverse_times_y_inverse)),
inference(cp,[status(thm)],[t2637,t4356]) ).
cnf(t5078,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = x_plus_y,
inference(orient,[status(thm)],[t4362]) ).
cnf(t5603,plain,
x_plus_y = multiply(inverse(x_inverse_times_y_inverse),multiplicative_identity),
inference(step,[status(thm)],[t5319,t5078]) ).
cnf(t5604,plain,
x_plus_y = inverse(x_inverse_times_y_inverse),
inference(step,[status(thm)],[t5603,t256]) ).
cnf(t5327,plain,
inverse(x_inverse_times_y_inverse) = x_plus_y,
inference(orient,[status(thm)],[t5604]) ).
cnf(f24,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f24_nnf,plain,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(g0_0,plain,
inverse(inverse(x_inverse_times_y_inverse)) != x_inverse_times_y_inverse,
inference(rw,[status(thm)],[goal_0,t5327]) ).
cnf(g0_1,plain,
x_inverse_times_y_inverse != x_inverse_times_y_inverse,
inference(rw,[status(thm)],[g0_0,t3198]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/15.39 % Computer : n017.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Fri Sep 25 06:27:21 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 52.74/22.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.74/22.91 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------