%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 12:59:37 PM UTC 2026
% Result : Unsatisfiable 42.22s 6.41s
% Output : Proof 42.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 23
% Syntax : Number of formulae : 299 ( 255 unt; 0 def)
% Number of atoms : 435 ( 224 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 279 ( 143 ~; 136 |; 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 : 597 ( 26 sgn 148 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(h7,plain,
product(V0,add(V1,V2),add(multiply(V0,V1),multiply(V0,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi1,hi1,hi0,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(h2,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(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(t236,plain,
add(multiply(add(X1,X2),X3),multiply(add(X1,X2),X2)) = add(multiply(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi21,h2,h7]) ).
cnf(f8,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(f8_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)],[f8]) ).
fof(f8_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)],[f8_nnf]) ).
cnf(c8,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)],[f8_sk]) ).
cnf(hi8,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)],[c8]) ).
cnf(h8,plain,
sum(multiply(V0,V1),multiply(V0,V2),multiply(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi8,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(h0,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(t195,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X3,X2)),
inference(hyper_resolution,[status(thm)],[hi20,h0,h8]) ).
cnf(t370,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X3,X2)),
inference(orient,[status(thm)],[t195]) ).
cnf(t11798,plain,
multiply(add(X1,X2),add(X2,X3)) = add(multiply(X1,X3),X2),
inference(step,[status(thm)],[t236,t370]) ).
cnf(t2060,plain,
multiply(add(X1,X2),add(X2,X3)) = add(multiply(X1,X3),X2),
inference(orient,[status(thm)],[t11798]) ).
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(h4,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(t235,plain,
add(multiply(add(X1,X2),X1),multiply(add(X1,X2),X3)) = add(X1,multiply(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi21,h4,h7]) ).
cnf(t11794,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(step,[status(thm)],[t235,t370]) ).
cnf(t1656,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t11794]) ).
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(t12,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi17]) ).
cnf(t2040,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t12]) ).
cnf(t2043,plain,
add(X1,multiply(inverse(X1),X2)) = multiply(multiplicative_identity,add(X2,X1)),
inference(cp,[status(thm)],[t1656,t2040]) ).
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(t10,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)],[t10]) ).
cnf(t11988,plain,
add(X1,multiply(inverse(X1),X2)) = add(X2,X1),
inference(step,[status(thm)],[t2043,t257]) ).
cnf(t8737,plain,
add(X1,multiply(inverse(X1),X2)) = add(X2,X1),
inference(orient,[status(thm)],[t11988]) ).
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(h16,plain,
product(V0,add(V1,V0),add(multiply(additive_identity,V1),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi4,hi0,hi1,hi0]) ).
cnf(f3,axiom,
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
fof(f3_nnf,plain,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h9,plain,
product(V0,V1,multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi1]) ).
cnf(t117,plain,
multiply(add(X1,X2),X2) = add(multiply(additive_identity,X1),X2),
inference(hyper_resolution,[status(thm)],[hi21,h9,h16]) ).
cnf(t196,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(add(X2,X3),X1),
inference(hyper_resolution,[status(thm)],[hi21,h7,h9]) ).
cnf(t11772,plain,
multiply(X1,add(X3,X2)) = multiply(add(X2,X3),X1),
inference(step,[status(thm)],[t196,t370]) ).
cnf(t845,plain,
multiply(X1,add(X2,X3)) = multiply(add(X3,X2),X1),
inference(orient,[status(thm)],[t11772]) ).
cnf(t11775,plain,
multiply(X2,add(X2,X1)) = add(multiply(additive_identity,X1),X2),
inference(step,[status(thm)],[t117,t845]) ).
cnf(t1012,plain,
add(multiply(additive_identity,X1),X2) = multiply(X2,add(X2,X1)),
inference(orient,[status(thm)],[t11775]) ).
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(h12,plain,
sum(multiply(V0,additive_identity),V1,multiply(add(V0,V1),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi0,hi4,hi1,hi1]) ).
cnf(t228,plain,
multiply(add(X1,multiply(X1,X2)),multiply(X1,X2)) = multiply(X1,add(additive_identity,X2)),
inference(hyper_resolution,[status(thm)],[hi20,h8,h12]) ).
cnf(t27,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(hyper_resolution,[status(thm)],[hi21,hi1,h9]) ).
cnf(t270,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t27]) ).
cnf(t11763,plain,
multiply(multiply(X1,X2),add(X1,multiply(X1,X2))) = multiply(X1,add(additive_identity,X2)),
inference(step,[status(thm)],[t228,t270]) ).
cnf(h13,plain,
sum(multiply(additive_identity,V0),V1,multiply(V1,add(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi4,hi0,hi1,hi1]) ).
cnf(t111,plain,
multiply(X1,add(X2,X1)) = add(multiply(additive_identity,X2),X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h13]) ).
cnf(t494,plain,
add(multiply(additive_identity,X1),X2) = multiply(X2,add(X1,X2)),
inference(orient,[status(thm)],[t111]) ).
cnf(t11764,plain,
add(multiply(additive_identity,X1),multiply(X1,X2)) = multiply(X1,add(additive_identity,X2)),
inference(step,[status(thm)],[t11763,t494]) ).
cnf(t3,plain,
add(additive_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi4]) ).
cnf(t259,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t11765,plain,
add(multiply(additive_identity,X1),multiply(X1,X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t11764,t259]) ).
cnf(t524,plain,
add(multiply(additive_identity,X1),multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t11765]) ).
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(t14,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi1,hi19]) ).
cnf(t548,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t14]) ).
cnf(t551,plain,
multiply(X1,inverse(X1)) = add(multiply(additive_identity,X1),additive_identity),
inference(cp,[status(thm)],[t524,t548]) ).
cnf(t11845,plain,
additive_identity = add(multiply(additive_identity,X1),additive_identity),
inference(step,[status(thm)],[t551,t548]) ).
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(t11846,plain,
additive_identity = multiply(additive_identity,X1),
inference(step,[status(thm)],[t11845,t258]) ).
cnf(t3446,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t11846]) ).
cnf(t11859,plain,
add(additive_identity,X2) = multiply(X2,add(X2,X1)),
inference(step,[status(thm)],[t1012,t3446]) ).
cnf(t11860,plain,
X2 = multiply(X2,add(X2,X1)),
inference(step,[status(thm)],[t11859,t259]) ).
cnf(t3467,plain,
X2 = multiply(X2,add(X2,X1)),
inference(rw,[status(thm)],[t11860]) ).
cnf(t3589,plain,
multiply(X1,add(X1,X2)) = X1,
inference(orient,[status(thm)],[t3467]) ).
cnf(t8755,plain,
add(add(inverse(X1),X2),X1) = add(X1,inverse(X1)),
inference(cp,[status(thm)],[t8737,t3589]) ).
cnf(t21,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h0]) ).
cnf(t1624,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t21]) ).
cnf(t11995,plain,
add(X1,add(inverse(X1),X2)) = add(X1,inverse(X1)),
inference(step,[status(thm)],[t8755,t1624]) ).
cnf(t11996,plain,
add(X1,add(inverse(X1),X2)) = multiplicative_identity,
inference(step,[status(thm)],[t11995,t2040]) ).
cnf(t8815,plain,
add(X1,add(inverse(X1),X2)) = multiplicative_identity,
inference(orient,[status(thm)],[t11996]) ).
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(h6,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(t114,plain,
multiply(add(X1,X1),X2) = multiply(X1,add(X2,X2)),
inference(hyper_resolution,[status(thm)],[hi20,h6,h8]) ).
cnf(t409,plain,
multiply(X1,add(X2,X2)) = multiply(add(X1,X1),X2),
inference(orient,[status(thm)],[t114]) ).
cnf(t3592,plain,
multiplicative_identity = add(multiplicative_identity,X1),
inference(cp,[status(thm)],[t3589,t257]) ).
cnf(t3609,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(orient,[status(thm)],[t3592]) ).
cnf(t3620,plain,
multiply(multiplicative_identity,add(X1,X1)) = multiply(multiplicative_identity,X1),
inference(cp,[status(thm)],[t409,t3609]) ).
cnf(t11880,plain,
add(X1,X1) = multiply(multiplicative_identity,X1),
inference(step,[status(thm)],[t3620,t257]) ).
cnf(t11881,plain,
add(X1,X1) = X1,
inference(step,[status(thm)],[t11880,t257]) ).
cnf(t3638,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t11881]) ).
cnf(t3645,plain,
add(multiply(X1,X2),X1) = multiply(X1,add(X1,X2)),
inference(cp,[status(thm)],[t2060,t3638]) ).
cnf(t3903,plain,
add(X1,multiply(X2,X1)) = X1,
inference(orient,[status(thm)],[t3645]) ).
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(h5,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(t198,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(X2,add(X1,X3)),
inference(hyper_resolution,[status(thm)],[hi21,h5,h9]) ).
cnf(t349,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(X2,add(X1,X3)),
inference(orient,[status(thm)],[t198]) ).
cnf(t11861,plain,
add(additive_identity,X2) = multiply(X2,add(X1,X2)),
inference(step,[status(thm)],[t494,t3446]) ).
cnf(t11862,plain,
X2 = multiply(X2,add(X1,X2)),
inference(step,[status(thm)],[t11861,t259]) ).
cnf(t3468,plain,
X2 = multiply(X2,add(X1,X2)),
inference(rw,[status(thm)],[t11862]) ).
cnf(t3830,plain,
multiply(X1,add(X2,X1)) = X1,
inference(orient,[status(thm)],[t3468]) ).
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(t6,plain,
add(y,x) = x_plus_y,
inference(hyper_resolution,[status(thm)],[hi20,hi24,h0]) ).
cnf(t2298,plain,
add(y,x) = x_plus_y,
inference(orient,[status(thm)],[t6]) ).
cnf(t3832,plain,
x = multiply(x,x_plus_y),
inference(cp,[status(thm)],[t3830,t2298]) ).
cnf(t11883,plain,
x = multiply(x_plus_y,x),
inference(step,[status(thm)],[t3832,t270]) ).
cnf(t3845,plain,
multiply(x_plus_y,x) = x,
inference(orient,[status(thm)],[t11883]) ).
cnf(t3849,plain,
multiply(x,add(x_plus_y,X1)) = add(x,multiply(X1,x)),
inference(cp,[status(thm)],[t349,t3845]) ).
cnf(t11920,plain,
multiply(x,add(x_plus_y,X1)) = x,
inference(step,[status(thm)],[t3849,t3903]) ).
cnf(t5748,plain,
multiply(x,add(x_plus_y,X1)) = x,
inference(orient,[status(thm)],[t11920]) ).
cnf(t194,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi21,hi1,h7]) ).
cnf(t11762,plain,
multiply(X1,add(X3,X2)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t194,t370]) ).
cnf(t390,plain,
multiply(X1,add(X2,X3)) = multiply(X1,add(X3,X2)),
inference(orient,[status(thm)],[t11762]) ).
cnf(t5749,plain,
x = multiply(x,add(X1,x_plus_y)),
inference(cp,[status(thm)],[t5748,t390]) ).
cnf(t5775,plain,
multiply(x,add(X1,x_plus_y)) = x,
inference(orient,[status(thm)],[t5749]) ).
cnf(t5783,plain,
add(X1,x_plus_y) = add(add(X1,x_plus_y),x),
inference(cp,[status(thm)],[t3903,t5775]) ).
cnf(t11922,plain,
add(X1,x_plus_y) = add(x,add(X1,x_plus_y)),
inference(step,[status(thm)],[t5783,t1624]) ).
cnf(t5822,plain,
add(x,add(X1,x_plus_y)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t11922]) ).
cnf(t8817,plain,
multiplicative_identity = add(inverse(x),x_plus_y),
inference(cp,[status(thm)],[t8815,t5822]) ).
cnf(t11997,plain,
multiplicative_identity = add(x_plus_y,inverse(x)),
inference(step,[status(thm)],[t8817,t1624]) ).
cnf(t8841,plain,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(orient,[status(thm)],[t11997]) ).
cnf(t8846,plain,
add(multiply(X1,inverse(x)),x_plus_y) = multiply(add(X1,x_plus_y),multiplicative_identity),
inference(cp,[status(thm)],[t2060,t8841]) ).
cnf(t11363,plain,
add(x_plus_y,multiply(inverse(x),X1)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t8846]) ).
cnf(t553,plain,
multiply(X1,add(inverse(X1),X2)) = add(multiply(X1,X2),additive_identity),
inference(cp,[status(thm)],[t370,t548]) ).
cnf(t11979,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t553,t258]) ).
cnf(t8227,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t11979]) ).
cnf(t11373,plain,
add(add(inverse(inverse(x)),X1),x_plus_y) = add(x_plus_y,multiply(inverse(x),X1)),
inference(cp,[status(thm)],[t11363,t8227]) ).
cnf(t12077,plain,
add(x_plus_y,add(inverse(inverse(x)),X1)) = add(x_plus_y,multiply(inverse(x),X1)),
inference(step,[status(thm)],[t11373,t1624]) ).
cnf(f22,axiom,
inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
fof(f22_nnf,plain,
! [X] : inverse(inverse(X)) = X,
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X] : inverse(inverse(X)) = X,
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t7,plain,
inverse(inverse(X1)) = X1,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t260,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t12078,plain,
add(x_plus_y,add(x,X1)) = add(x_plus_y,multiply(inverse(x),X1)),
inference(step,[status(thm)],[t12077,t260]) ).
cnf(t12079,plain,
add(x_plus_y,add(x,X1)) = add(X1,x_plus_y),
inference(step,[status(thm)],[t12078,t11363]) ).
cnf(t11421,plain,
add(x_plus_y,add(x,X1)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t12079]) ).
cnf(t206,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X3,X2)),
inference(hyper_resolution,[status(thm)],[hi21,h4,h9]) ).
cnf(t1297,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t206]) ).
cnf(t2045,plain,
add(X1,multiply(X2,inverse(X1))) = multiply(multiplicative_identity,add(X1,X2)),
inference(cp,[status(thm)],[t1297,t2040]) ).
cnf(t12029,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(step,[status(thm)],[t2045,t257]) ).
cnf(t10070,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(orient,[status(thm)],[t12029]) ).
cnf(f25,hypothesis,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
fof(f25_nnf,plain,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,axiom,
product(inverse(x),inverse(y),x_inverse_times_y_inverse) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t30,plain,
multiply(inverse(y),inverse(x)) = x_inverse_times_y_inverse,
inference(hyper_resolution,[status(thm)],[hi21,hi25,h9]) ).
cnf(t1606,plain,
multiply(inverse(y),inverse(x)) = x_inverse_times_y_inverse,
inference(orient,[status(thm)],[t30]) ).
cnf(t10090,plain,
add(x,inverse(y)) = add(x,x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t10070,t1606]) ).
cnf(t12030,plain,
add(x,inverse(y)) = add(x_inverse_times_y_inverse,x),
inference(step,[status(thm)],[t10090,t1624]) ).
cnf(t10122,plain,
add(x,inverse(y)) = add(x_inverse_times_y_inverse,x),
inference(orient,[status(thm)],[t12030]) ).
cnf(t11426,plain,
add(inverse(y),x_plus_y) = add(x_plus_y,add(x_inverse_times_y_inverse,x)),
inference(cp,[status(thm)],[t11421,t10122]) ).
cnf(t12087,plain,
add(x_plus_y,inverse(y)) = add(x_plus_y,add(x_inverse_times_y_inverse,x)),
inference(step,[status(thm)],[t11426,t1624]) ).
cnf(t3594,plain,
y = multiply(y,x_plus_y),
inference(cp,[status(thm)],[t3589,t2298]) ).
cnf(t3623,plain,
multiply(y,x_plus_y) = y,
inference(orient,[status(thm)],[t3594]) ).
cnf(t3625,plain,
multiply(y,add(X1,x_plus_y)) = add(y,multiply(y,X1)),
inference(cp,[status(thm)],[t370,t3623]) ).
cnf(t3913,plain,
X1 = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t3903,t270]) ).
cnf(t4021,plain,
add(X1,multiply(X1,X2)) = X1,
inference(orient,[status(thm)],[t3913]) ).
cnf(t11911,plain,
multiply(y,add(X1,x_plus_y)) = y,
inference(step,[status(thm)],[t3625,t4021]) ).
cnf(t5391,plain,
multiply(y,add(X1,x_plus_y)) = y,
inference(orient,[status(thm)],[t11911]) ).
cnf(t5402,plain,
add(X1,x_plus_y) = add(add(X1,x_plus_y),y),
inference(cp,[status(thm)],[t3903,t5391]) ).
cnf(t11912,plain,
add(X1,x_plus_y) = add(y,add(X1,x_plus_y)),
inference(step,[status(thm)],[t5402,t1624]) ).
cnf(t5430,plain,
add(y,add(X1,x_plus_y)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t11912]) ).
cnf(t8818,plain,
multiplicative_identity = add(inverse(y),x_plus_y),
inference(cp,[status(thm)],[t8815,t5430]) ).
cnf(t11998,plain,
multiplicative_identity = add(x_plus_y,inverse(y)),
inference(step,[status(thm)],[t8818,t1624]) ).
cnf(t8857,plain,
add(x_plus_y,inverse(y)) = multiplicative_identity,
inference(orient,[status(thm)],[t11998]) ).
cnf(t12088,plain,
multiplicative_identity = add(x_plus_y,add(x_inverse_times_y_inverse,x)),
inference(step,[status(thm)],[t12087,t8857]) ).
cnf(t552,plain,
multiply(X1,add(X2,inverse(X1))) = add(additive_identity,multiply(X1,X2)),
inference(cp,[status(thm)],[t370,t548]) ).
cnf(t11923,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(step,[status(thm)],[t552,t259]) ).
cnf(t5945,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(orient,[status(thm)],[t11923]) ).
cnf(t11379,plain,
add(add(X1,inverse(inverse(x))),x_plus_y) = add(x_plus_y,multiply(inverse(x),X1)),
inference(cp,[status(thm)],[t11363,t5945]) ).
cnf(t12080,plain,
add(x_plus_y,add(X1,inverse(inverse(x)))) = add(x_plus_y,multiply(inverse(x),X1)),
inference(step,[status(thm)],[t11379,t1624]) ).
cnf(t12081,plain,
add(x_plus_y,add(X1,x)) = add(x_plus_y,multiply(inverse(x),X1)),
inference(step,[status(thm)],[t12080,t260]) ).
cnf(t12082,plain,
add(x_plus_y,add(X1,x)) = add(X1,x_plus_y),
inference(step,[status(thm)],[t12081,t11363]) ).
cnf(t11467,plain,
add(x_plus_y,add(X1,x)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t12082]) ).
cnf(t12089,plain,
multiplicative_identity = add(x_inverse_times_y_inverse,x_plus_y),
inference(step,[status(thm)],[t12088,t11467]) ).
cnf(t12090,plain,
multiplicative_identity = add(x_plus_y,x_inverse_times_y_inverse),
inference(step,[status(thm)],[t12089,t1624]) ).
cnf(t11581,plain,
add(x_plus_y,x_inverse_times_y_inverse) = multiplicative_identity,
inference(orient,[status(thm)],[t12090]) ).
cnf(t11585,plain,
add(multiply(X1,x_inverse_times_y_inverse),x_plus_y) = multiply(add(X1,x_plus_y),multiplicative_identity),
inference(cp,[status(thm)],[t2060,t11581]) ).
cnf(t11675,plain,
add(x_plus_y,multiply(x_inverse_times_y_inverse,X1)) = add(X1,x_plus_y),
inference(orient,[status(thm)],[t11585]) ).
cnf(t11718,plain,
add(inverse(x_inverse_times_y_inverse),x_plus_y) = add(x_plus_y,additive_identity),
inference(cp,[status(thm)],[t11675,t548]) ).
cnf(t12091,plain,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = add(x_plus_y,additive_identity),
inference(step,[status(thm)],[t11718,t1624]) ).
cnf(t3908,plain,
inverse(x) = add(inverse(x),x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t3903,t1606]) ).
cnf(t11887,plain,
inverse(x) = add(x_inverse_times_y_inverse,inverse(x)),
inference(step,[status(thm)],[t3908,t1624]) ).
cnf(t3994,plain,
add(x_inverse_times_y_inverse,inverse(x)) = inverse(x),
inference(orient,[status(thm)],[t11887]) ).
cnf(t5950,plain,
multiply(x,x_inverse_times_y_inverse) = multiply(x,inverse(x)),
inference(cp,[status(thm)],[t5945,t3994]) ).
cnf(t11925,plain,
multiply(x_inverse_times_y_inverse,x) = multiply(x,inverse(x)),
inference(step,[status(thm)],[t5950,t270]) ).
cnf(t11926,plain,
multiply(x_inverse_times_y_inverse,x) = additive_identity,
inference(step,[status(thm)],[t11925,t548]) ).
cnf(t5975,plain,
multiply(x_inverse_times_y_inverse,x) = additive_identity,
inference(orient,[status(thm)],[t11926]) ).
cnf(t5979,plain,
multiply(x_inverse_times_y_inverse,add(X1,x)) = add(additive_identity,multiply(x_inverse_times_y_inverse,X1)),
inference(cp,[status(thm)],[t370,t5975]) ).
cnf(t11930,plain,
multiply(x_inverse_times_y_inverse,add(X1,x)) = multiply(x_inverse_times_y_inverse,X1),
inference(step,[status(thm)],[t5979,t259]) ).
cnf(t6141,plain,
multiply(x_inverse_times_y_inverse,add(X1,x)) = multiply(x_inverse_times_y_inverse,X1),
inference(orient,[status(thm)],[t11930]) ).
cnf(t6143,plain,
multiply(x_inverse_times_y_inverse,y) = multiply(x_inverse_times_y_inverse,x_plus_y),
inference(cp,[status(thm)],[t6141,t2298]) ).
cnf(t11931,plain,
multiply(y,x_inverse_times_y_inverse) = multiply(x_inverse_times_y_inverse,x_plus_y),
inference(step,[status(thm)],[t6143,t270]) ).
cnf(t4024,plain,
inverse(y) = add(inverse(y),x_inverse_times_y_inverse),
inference(cp,[status(thm)],[t4021,t1606]) ).
cnf(t11889,plain,
inverse(y) = add(x_inverse_times_y_inverse,inverse(y)),
inference(step,[status(thm)],[t4024,t1624]) ).
cnf(t4108,plain,
add(x_inverse_times_y_inverse,inverse(y)) = inverse(y),
inference(orient,[status(thm)],[t11889]) ).
cnf(t5951,plain,
multiply(y,x_inverse_times_y_inverse) = multiply(y,inverse(y)),
inference(cp,[status(thm)],[t5945,t4108]) ).
cnf(t11927,plain,
multiply(y,x_inverse_times_y_inverse) = additive_identity,
inference(step,[status(thm)],[t5951,t548]) ).
cnf(t5986,plain,
multiply(y,x_inverse_times_y_inverse) = additive_identity,
inference(orient,[status(thm)],[t11927]) ).
cnf(t11932,plain,
additive_identity = multiply(x_inverse_times_y_inverse,x_plus_y),
inference(step,[status(thm)],[t11931,t5986]) ).
cnf(t11933,plain,
additive_identity = multiply(x_plus_y,x_inverse_times_y_inverse),
inference(step,[status(thm)],[t11932,t270]) ).
cnf(t6160,plain,
multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
inference(orient,[status(thm)],[t11933]) ).
cnf(t6165,plain,
multiply(x_plus_y,add(x_inverse_times_y_inverse,X1)) = add(multiply(x_plus_y,X1),additive_identity),
inference(cp,[status(thm)],[t370,t6160]) ).
cnf(t11952,plain,
multiply(x_plus_y,add(x_inverse_times_y_inverse,X1)) = multiply(x_plus_y,X1),
inference(step,[status(thm)],[t6165,t258]) ).
cnf(t6621,plain,
multiply(x_plus_y,add(x_inverse_times_y_inverse,X1)) = multiply(x_plus_y,X1),
inference(orient,[status(thm)],[t11952]) ).
cnf(t6624,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = multiply(x_plus_y,multiplicative_identity),
inference(cp,[status(thm)],[t6621,t2040]) ).
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(t8,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)],[t8]) ).
cnf(t11953,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = x_plus_y,
inference(step,[status(thm)],[t6624,t256]) ).
cnf(t6641,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = x_plus_y,
inference(orient,[status(thm)],[t11953]) ).
cnf(t6648,plain,
inverse(x_inverse_times_y_inverse) = add(inverse(x_inverse_times_y_inverse),x_plus_y),
inference(cp,[status(thm)],[t3903,t6641]) ).
cnf(t11954,plain,
inverse(x_inverse_times_y_inverse) = add(x_plus_y,inverse(x_inverse_times_y_inverse)),
inference(step,[status(thm)],[t6648,t1624]) ).
cnf(t6659,plain,
add(x_plus_y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(orient,[status(thm)],[t11954]) ).
cnf(t12092,plain,
inverse(x_inverse_times_y_inverse) = add(x_plus_y,additive_identity),
inference(step,[status(thm)],[t12091,t6659]) ).
cnf(t12093,plain,
inverse(x_inverse_times_y_inverse) = x_plus_y,
inference(step,[status(thm)],[t12092,t258]) ).
cnf(t11744,plain,
inverse(x_inverse_times_y_inverse) = x_plus_y,
inference(orient,[status(thm)],[t12093]) ).
cnf(f26,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f26_nnf,plain,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(g0_0,plain,
inverse(inverse(x_inverse_times_y_inverse)) != x_inverse_times_y_inverse,
inference(rw,[status(thm)],[goal_0,t11744]) ).
cnf(g0_1,plain,
x_inverse_times_y_inverse != x_inverse_times_y_inverse,
inference(rw,[status(thm)],[g0_0,t260]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 06:32:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.22/6.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.22/6.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------