%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO015-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 73.24s 9.74s
% Output : Proof 73.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 24
% Syntax : Number of formulae : 443 ( 403 unt; 0 def)
% Number of atoms : 563 ( 364 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 ( 2 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 : 567 ( 4 sgn 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity8) ).
fof(f15_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(product(X0,X3,X5),true,ifeq(product(X2,X4,X6),true,sum(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f0,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f0_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f1,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f1_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h5,plain,
sum(multiply(V0,V1),V2,multiply(add(V0,V2),add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi0,hi0,hi1,hi1]) ).
cnf(f2,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0]) ).
cnf(f20,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f20_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t216,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(hyper_resolution,[status(thm)],[hi20,h1,h5]) ).
cnf(t268,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(orient,[status(thm)],[t216]) ).
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(t8,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi17]) ).
cnf(t266,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t8]) ).
cnf(t269,plain,
add(inverse(X1),multiply(X1,X2)) = multiply(multiplicative_identity,add(X2,inverse(X1))),
inference(cp,[status(thm)],[t268,t266]) ).
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(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(h14,plain,
product(V0,V1,add(additive_identity,multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi4,hi4,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(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(t19,plain,
add(additive_identity,multiply(multiplicative_identity,X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi21,hi6,h14]) ).
cnf(t3,plain,
add(additive_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi20,hi4,hi0]) ).
cnf(t257,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t23622,plain,
multiply(multiplicative_identity,X1) = X1,
inference(step,[status(thm)],[t19,t257]) ).
cnf(t259,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t23622]) ).
cnf(t23696,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(step,[status(thm)],[t269,t259]) ).
cnf(t2614,plain,
add(inverse(X1),multiply(X1,X2)) = add(X2,inverse(X1)),
inference(orient,[status(thm)],[t23696]) ).
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(t32,plain,
add(additive_identity,multiply(inverse(X1),X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi18,h14]) ).
cnf(t23628,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(step,[status(thm)],[t32,t257]) ).
cnf(t416,plain,
multiply(inverse(X1),X1) = additive_identity,
inference(orient,[status(thm)],[t23628]) ).
cnf(t2621,plain,
add(X1,inverse(inverse(X1))) = add(inverse(inverse(X1)),additive_identity),
inference(cp,[status(thm)],[t2614,t416]) ).
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(t214,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h13]) ).
cnf(t275,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t214]) ).
cnf(t278,plain,
add(X1,multiply(inverse(X1),X2)) = multiply(multiplicative_identity,add(X1,X2)),
inference(cp,[status(thm)],[t275,t266]) ).
cnf(t23681,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(step,[status(thm)],[t278,t259]) ).
cnf(t2190,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(orient,[status(thm)],[t23681]) ).
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(t31,plain,
add(additive_identity,multiply(X1,inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi21,hi19,h14]) ).
cnf(t23627,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t31,t257]) ).
cnf(t412,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t23627]) ).
cnf(t2197,plain,
add(X1,inverse(inverse(X1))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t2190,t412]) ).
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(t256,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t23684,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(step,[status(thm)],[t2197,t256]) ).
cnf(t2315,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(orient,[status(thm)],[t23684]) ).
cnf(t23697,plain,
X1 = add(inverse(inverse(X1)),additive_identity),
inference(step,[status(thm)],[t2621,t2315]) ).
cnf(t23698,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t23697,t256]) ).
cnf(t2641,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t23698]) ).
cnf(t17,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi20,hi0,h1]) ).
cnf(t265,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t17]) ).
cnf(t271,plain,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X3,X1)),
inference(cp,[status(thm)],[t268,t265]) ).
cnf(t3664,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t271]) ).
cnf(t2209,plain,
add(X1,multiply(multiply(inverse(X1),X2),X3)) = multiply(add(X1,X2),add(X1,X3)),
inference(cp,[status(thm)],[t275,t2190]) ).
cnf(t24052,plain,
add(X1,multiply(multiply(inverse(X1),X2),X3)) = add(X1,multiply(X2,X3)),
inference(step,[status(thm)],[t2209,t275]) ).
cnf(t13355,plain,
add(X1,multiply(multiply(inverse(X1),X2),X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t24052]) ).
cnf(t13369,plain,
add(X1,multiply(X2,inverse(multiply(inverse(X1),X2)))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t13355,t412]) ).
cnf(t24053,plain,
add(X1,multiply(X2,inverse(multiply(inverse(X1),X2)))) = X1,
inference(step,[status(thm)],[t13369,t256]) ).
cnf(t13424,plain,
add(X1,multiply(X2,inverse(multiply(inverse(X1),X2)))) = X1,
inference(orient,[status(thm)],[t24053]) ).
cnf(t13457,plain,
inverse(X1) = add(inverse(X1),multiply(X2,inverse(multiply(X1,X2)))),
inference(cp,[status(thm)],[t13424,t2641]) ).
cnf(t13908,plain,
add(inverse(X1),multiply(X2,inverse(multiply(X1,X2)))) = inverse(X1),
inference(orient,[status(thm)],[t13457]) ).
cnf(f23,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_inverse_plus_y_inverse) ).
fof(f23_nnf,plain,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t21,plain,
add(inverse(x),inverse(y)) = x_inverse_plus_y_inverse,
inference(hyper_resolution,[status(thm)],[hi20,hi0,hi23]) ).
cnf(t23623,plain,
add(inverse(y),inverse(x)) = x_inverse_plus_y_inverse,
inference(step,[status(thm)],[t21,t265]) ).
cnf(t319,plain,
add(inverse(y),inverse(x)) = x_inverse_plus_y_inverse,
inference(orient,[status(thm)],[t23623]) ).
cnf(t320,plain,
add(inverse(y),multiply(inverse(x),X1)) = multiply(x_inverse_plus_y_inverse,add(inverse(y),X1)),
inference(cp,[status(thm)],[t275,t319]) ).
cnf(t9407,plain,
add(inverse(y),multiply(inverse(x),X1)) = multiply(x_inverse_plus_y_inverse,add(inverse(y),X1)),
inference(orient,[status(thm)],[t320]) ).
cnf(t9412,plain,
multiply(x_inverse_plus_y_inverse,add(inverse(y),x)) = add(inverse(y),additive_identity),
inference(cp,[status(thm)],[t9407,t416]) ).
cnf(t23942,plain,
multiply(x_inverse_plus_y_inverse,add(x,inverse(y))) = add(inverse(y),additive_identity),
inference(step,[status(thm)],[t9412,t265]) ).
cnf(t272,plain,
add(inverse(X1),multiply(X2,X1)) = multiply(add(X2,inverse(X1)),multiplicative_identity),
inference(cp,[status(thm)],[t268,t266]) ).
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(t18,plain,
add(additive_identity,multiply(X1,multiplicative_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi21,hi7,h14]) ).
cnf(t23621,plain,
multiply(X1,multiplicative_identity) = X1,
inference(step,[status(thm)],[t18,t257]) ).
cnf(t258,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t23621]) ).
cnf(t23704,plain,
add(inverse(X1),multiply(X2,X1)) = add(X2,inverse(X1)),
inference(step,[status(thm)],[t272,t258]) ).
cnf(t2660,plain,
add(inverse(X1),multiply(X2,X1)) = add(X2,inverse(X1)),
inference(orient,[status(thm)],[t23704]) ).
cnf(f22,negated_conjecture,
product(x,y,x_times_y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_y) ).
fof(f22_nnf,plain,
product(x,y,x_times_y),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
product(x,y,x_times_y),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,negated_conjecture,
product(x,y,x_times_y) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t20,plain,
add(additive_identity,multiply(x,y)) = x_times_y,
inference(hyper_resolution,[status(thm)],[hi21,hi22,h14]) ).
cnf(t23629,plain,
multiply(x,y) = x_times_y,
inference(step,[status(thm)],[t20,t257]) ).
cnf(t420,plain,
multiply(x,y) = x_times_y,
inference(orient,[status(thm)],[t23629]) ).
cnf(t2665,plain,
add(x,inverse(y)) = add(inverse(y),x_times_y),
inference(cp,[status(thm)],[t2660,t420]) ).
cnf(t23705,plain,
add(x,inverse(y)) = add(x_times_y,inverse(y)),
inference(step,[status(thm)],[t2665,t265]) ).
cnf(t2687,plain,
add(x,inverse(y)) = add(x_times_y,inverse(y)),
inference(orient,[status(thm)],[t23705]) ).
cnf(t23943,plain,
multiply(x_inverse_plus_y_inverse,add(x_times_y,inverse(y))) = add(inverse(y),additive_identity),
inference(step,[status(thm)],[t23942,t2687]) ).
cnf(t23944,plain,
multiply(x_inverse_plus_y_inverse,add(x_times_y,inverse(y))) = inverse(y),
inference(step,[status(thm)],[t23943,t256]) ).
cnf(t9443,plain,
multiply(x_inverse_plus_y_inverse,add(x_times_y,inverse(y))) = inverse(y),
inference(orient,[status(thm)],[t23944]) ).
cnf(t13935,plain,
inverse(x_inverse_plus_y_inverse) = add(inverse(x_inverse_plus_y_inverse),multiply(add(x_times_y,inverse(y)),inverse(inverse(y)))),
inference(cp,[status(thm)],[t13908,t9443]) ).
cnf(t24065,plain,
inverse(x_inverse_plus_y_inverse) = add(inverse(x_inverse_plus_y_inverse),multiply(add(x_times_y,inverse(y)),y)),
inference(step,[status(thm)],[t13935,t2641]) ).
cnf(t243,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t263,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t243]) ).
cnf(t15,plain,
sum(X1,additive_identity,X1) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t535,plain,
sum(X1,additive_identity,X1) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t537,plain,
X1 = ifeq(sum(X1,additive_identity,X2),true,ifeq(true,true,X2,X1),X1),
inference(cp,[status(thm)],[t263,t535]) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t260,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t23766,plain,
X1 = ifeq(sum(X1,additive_identity,X2),true,X2,X1),
inference(step,[status(thm)],[t537,t260]) ).
cnf(t3572,plain,
ifeq(sum(X1,additive_identity,X2),true,X2,X1) = X1,
inference(orient,[status(thm)],[t23766]) ).
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(t228,plain,
sum(x_times_y,additive_identity,add(additive_identity,multiply(add(inverse(y),x),y))) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi22,hi18,h1,h14]) ).
cnf(t23671,plain,
sum(x_times_y,additive_identity,multiply(add(inverse(y),x),y)) = true,
inference(step,[status(thm)],[t228,t257]) ).
cnf(t23672,plain,
sum(x_times_y,additive_identity,multiply(add(x,inverse(y)),y)) = true,
inference(step,[status(thm)],[t23671,t265]) ).
cnf(t629,plain,
sum(x_times_y,additive_identity,multiply(add(x,inverse(y)),y)) = true,
inference(orient,[status(thm)],[t23672]) ).
cnf(t23710,plain,
sum(x_times_y,additive_identity,multiply(add(x_times_y,inverse(y)),y)) = true,
inference(step,[status(thm)],[t629,t2687]) ).
cnf(t2703,plain,
sum(x_times_y,additive_identity,multiply(add(x_times_y,inverse(y)),y)) = true,
inference(rw,[status(thm)],[t23710]) ).
cnf(t7312,plain,
sum(x_times_y,additive_identity,multiply(add(x_times_y,inverse(y)),y)) = true,
inference(orient,[status(thm)],[t2703]) ).
cnf(t7313,plain,
x_times_y = ifeq(true,true,multiply(add(x_times_y,inverse(y)),y),x_times_y),
inference(cp,[status(thm)],[t3572,t7312]) ).
cnf(t23912,plain,
x_times_y = multiply(add(x_times_y,inverse(y)),y),
inference(step,[status(thm)],[t7313,t260]) ).
cnf(t7339,plain,
multiply(add(x_times_y,inverse(y)),y) = x_times_y,
inference(orient,[status(thm)],[t23912]) ).
cnf(t24066,plain,
inverse(x_inverse_plus_y_inverse) = add(inverse(x_inverse_plus_y_inverse),x_times_y),
inference(step,[status(thm)],[t24065,t7339]) ).
cnf(t24067,plain,
inverse(x_inverse_plus_y_inverse) = add(x_times_y,inverse(x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t24066,t265]) ).
cnf(t14013,plain,
add(x_times_y,inverse(x_inverse_plus_y_inverse)) = inverse(x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t24067]) ).
cnf(t14016,plain,
add(x_times_y,multiply(inverse(x_inverse_plus_y_inverse),X1)) = multiply(inverse(x_inverse_plus_y_inverse),add(X1,x_times_y)),
inference(cp,[status(thm)],[t3664,t14013]) ).
cnf(t14473,plain,
add(x_times_y,multiply(inverse(x_inverse_plus_y_inverse),X1)) = multiply(inverse(x_inverse_plus_y_inverse),add(X1,x_times_y)),
inference(orient,[status(thm)],[t14016]) ).
cnf(t14482,plain,
multiply(inverse(x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,x_times_y)) = add(x_times_y,additive_identity),
inference(cp,[status(thm)],[t14473,t416]) ).
cnf(t24086,plain,
multiply(inverse(x_inverse_plus_y_inverse),add(x_times_y,x_inverse_plus_y_inverse)) = add(x_times_y,additive_identity),
inference(step,[status(thm)],[t14482,t265]) ).
cnf(t24087,plain,
multiply(inverse(x_inverse_plus_y_inverse),add(x_times_y,x_inverse_plus_y_inverse)) = x_times_y,
inference(step,[status(thm)],[t24086,t256]) ).
cnf(t14518,plain,
multiply(inverse(x_inverse_plus_y_inverse),add(x_times_y,x_inverse_plus_y_inverse)) = x_times_y,
inference(orient,[status(thm)],[t24087]) ).
cnf(t274,plain,
add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X1,X3)),
inference(cp,[status(thm)],[t268,t265]) ).
cnf(t4534,plain,
multiply(add(X1,X2),add(X2,X3)) = add(X2,multiply(X1,X3)),
inference(orient,[status(thm)],[t274]) ).
cnf(t14015,plain,
add(x_times_y,multiply(X1,inverse(x_inverse_plus_y_inverse))) = multiply(add(X1,x_times_y),inverse(x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t4534,t14013]) ).
cnf(t14253,plain,
add(x_times_y,multiply(X1,inverse(x_inverse_plus_y_inverse))) = multiply(add(X1,x_times_y),inverse(x_inverse_plus_y_inverse)),
inference(orient,[status(thm)],[t14015]) ).
cnf(t14261,plain,
multiply(add(x_inverse_plus_y_inverse,x_times_y),inverse(x_inverse_plus_y_inverse)) = add(x_times_y,additive_identity),
inference(cp,[status(thm)],[t14253,t412]) ).
cnf(t24074,plain,
multiply(add(x_times_y,x_inverse_plus_y_inverse),inverse(x_inverse_plus_y_inverse)) = add(x_times_y,additive_identity),
inference(step,[status(thm)],[t14261,t265]) ).
cnf(t24075,plain,
multiply(add(x_times_y,x_inverse_plus_y_inverse),inverse(x_inverse_plus_y_inverse)) = x_times_y,
inference(step,[status(thm)],[t24074,t256]) ).
cnf(t14295,plain,
multiply(add(x_times_y,x_inverse_plus_y_inverse),inverse(x_inverse_plus_y_inverse)) = x_times_y,
inference(orient,[status(thm)],[t24075]) ).
cnf(t14296,plain,
add(add(x_times_y,x_inverse_plus_y_inverse),inverse(inverse(x_inverse_plus_y_inverse))) = add(inverse(inverse(x_inverse_plus_y_inverse)),x_times_y),
inference(cp,[status(thm)],[t2660,t14295]) ).
cnf(t24076,plain,
add(add(x_times_y,x_inverse_plus_y_inverse),x_inverse_plus_y_inverse) = add(inverse(inverse(x_inverse_plus_y_inverse)),x_times_y),
inference(step,[status(thm)],[t14296,t2641]) ).
cnf(t24077,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x_inverse_plus_y_inverse)) = add(inverse(inverse(x_inverse_plus_y_inverse)),x_times_y),
inference(step,[status(thm)],[t24076,t265]) ).
cnf(t24078,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x_inverse_plus_y_inverse)) = add(x_times_y,inverse(inverse(x_inverse_plus_y_inverse))),
inference(step,[status(thm)],[t24077,t265]) ).
cnf(t24079,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x_inverse_plus_y_inverse)) = add(x_times_y,x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t24078,t2641]) ).
cnf(t14309,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x_inverse_plus_y_inverse)) = add(x_times_y,x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t24079]) ).
cnf(t14312,plain,
add(x_inverse_plus_y_inverse,multiply(add(x_times_y,x_inverse_plus_y_inverse),X1)) = multiply(add(x_times_y,x_inverse_plus_y_inverse),add(X1,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t3664,t14309]) ).
cnf(t24096,plain,
add(x_inverse_plus_y_inverse,multiply(add(x_times_y,x_inverse_plus_y_inverse),X1)) = add(x_inverse_plus_y_inverse,multiply(x_times_y,X1)),
inference(step,[status(thm)],[t14312,t268]) ).
cnf(t14923,plain,
add(x_inverse_plus_y_inverse,multiply(add(x_times_y,x_inverse_plus_y_inverse),X1)) = add(x_inverse_plus_y_inverse,multiply(x_times_y,X1)),
inference(orient,[status(thm)],[t24096]) ).
cnf(t14936,plain,
add(x_inverse_plus_y_inverse,multiply(x_times_y,add(X1,x_times_y))) = add(x_inverse_plus_y_inverse,add(x_times_y,multiply(x_inverse_plus_y_inverse,X1))),
inference(cp,[status(thm)],[t14923,t3664]) ).
cnf(t16031,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,multiply(x_inverse_plus_y_inverse,X1))) = add(x_inverse_plus_y_inverse,multiply(x_times_y,add(X1,x_times_y))),
inference(orient,[status(thm)],[t14936]) ).
cnf(t242,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t261,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t242]) ).
cnf(t13,plain,
product(multiplicative_identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t505,plain,
product(multiplicative_identity,X1,X1) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t506,plain,
X1 = ifeq(true,true,ifeq(product(multiplicative_identity,X2,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t261,t505]) ).
cnf(t23724,plain,
X1 = ifeq(product(multiplicative_identity,X2,X1),true,X2,X1),
inference(step,[status(thm)],[t506,t260]) ).
cnf(t2895,plain,
ifeq(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t23724]) ).
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(f16,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f16_nnf,plain,
! [X] : sum(inverse(X),X,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : sum(inverse(X),X,multiplicative_identity),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
sum(inverse(X0),X0,multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t123,plain,
product(multiplicative_identity,y,add(multiply(inverse(x),y),x_times_y)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi1,hi22,hi16,hi0]) ).
cnf(t23653,plain,
product(multiplicative_identity,y,add(x_times_y,multiply(inverse(x),y))) = true,
inference(step,[status(thm)],[t123,t265]) ).
cnf(t511,plain,
product(multiplicative_identity,y,add(x_times_y,multiply(inverse(x),y))) = true,
inference(orient,[status(thm)],[t23653]) ).
cnf(t2896,plain,
add(x_times_y,multiply(inverse(x),y)) = ifeq(true,true,y,add(x_times_y,multiply(inverse(x),y))),
inference(cp,[status(thm)],[t2895,t511]) ).
cnf(t23725,plain,
add(x_times_y,multiply(inverse(x),y)) = y,
inference(step,[status(thm)],[t2896,t260]) ).
cnf(t2905,plain,
add(x_times_y,multiply(inverse(x),y)) = y,
inference(orient,[status(thm)],[t23725]) ).
cnf(t536,plain,
X1 = ifeq(true,true,ifeq(sum(X2,additive_identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t263,t535]) ).
cnf(t23727,plain,
X1 = ifeq(sum(X2,additive_identity,X1),true,X2,X1),
inference(step,[status(thm)],[t536,t260]) ).
cnf(t2968,plain,
ifeq(sum(X1,additive_identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t23727]) ).
cnf(t151,plain,
sum(multiply(inverse(x),y),additive_identity,multiply(x_inverse_plus_y_inverse,y)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi1,hi18,hi23,hi1]) ).
cnf(t587,plain,
sum(multiply(inverse(x),y),additive_identity,multiply(x_inverse_plus_y_inverse,y)) = true,
inference(orient,[status(thm)],[t151]) ).
cnf(t2973,plain,
multiply(x_inverse_plus_y_inverse,y) = ifeq(true,true,multiply(inverse(x),y),multiply(x_inverse_plus_y_inverse,y)),
inference(cp,[status(thm)],[t2968,t587]) ).
cnf(t23730,plain,
multiply(x_inverse_plus_y_inverse,y) = multiply(inverse(x),y),
inference(step,[status(thm)],[t2973,t260]) ).
cnf(t2991,plain,
multiply(inverse(x),y) = multiply(x_inverse_plus_y_inverse,y),
inference(orient,[status(thm)],[t23730]) ).
cnf(t23731,plain,
add(x_times_y,multiply(x_inverse_plus_y_inverse,y)) = y,
inference(step,[status(thm)],[t2905,t2991]) ).
cnf(t2999,plain,
add(x_times_y,multiply(x_inverse_plus_y_inverse,y)) = y,
inference(rw,[status(thm)],[t23731]) ).
cnf(t3003,plain,
add(x_times_y,multiply(x_inverse_plus_y_inverse,y)) = y,
inference(orient,[status(thm)],[t2999]) ).
cnf(t16033,plain,
add(x_inverse_plus_y_inverse,multiply(x_times_y,add(y,x_times_y))) = add(x_inverse_plus_y_inverse,y),
inference(cp,[status(thm)],[t16031,t3003]) ).
cnf(t24123,plain,
add(x_inverse_plus_y_inverse,multiply(x_times_y,add(y,x_times_y))) = add(y,x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t16033,t265]) ).
cnf(t16094,plain,
add(x_inverse_plus_y_inverse,multiply(x_times_y,add(y,x_times_y))) = add(y,x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t24123]) ).
cnf(t16,plain,
sum(additive_identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t596,plain,
sum(additive_identity,X1,X1) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t597,plain,
X1 = ifeq(true,true,ifeq(sum(additive_identity,X2,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t263,t596]) ).
cnf(t23767,plain,
X1 = ifeq(sum(additive_identity,X2,X1),true,X2,X1),
inference(step,[status(thm)],[t597,t260]) ).
cnf(t3573,plain,
ifeq(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t23767]) ).
cnf(t145,plain,
sum(additive_identity,multiply(inverse(y),x),multiply(x_inverse_plus_y_inverse,x)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi18,hi1,hi23,hi1]) ).
cnf(t605,plain,
sum(additive_identity,multiply(inverse(y),x),multiply(x_inverse_plus_y_inverse,x)) = true,
inference(orient,[status(thm)],[t145]) ).
cnf(t3574,plain,
multiply(x_inverse_plus_y_inverse,x) = ifeq(true,true,multiply(inverse(y),x),multiply(x_inverse_plus_y_inverse,x)),
inference(cp,[status(thm)],[t3573,t605]) ).
cnf(t23768,plain,
multiply(x_inverse_plus_y_inverse,x) = multiply(inverse(y),x),
inference(step,[status(thm)],[t3574,t260]) ).
cnf(t3584,plain,
multiply(inverse(y),x) = multiply(x_inverse_plus_y_inverse,x),
inference(orient,[status(thm)],[t23768]) ).
cnf(t3585,plain,
add(inverse(y),inverse(x)) = add(inverse(x),multiply(x_inverse_plus_y_inverse,x)),
inference(cp,[status(thm)],[t2660,t3584]) ).
cnf(t23770,plain,
x_inverse_plus_y_inverse = add(inverse(x),multiply(x_inverse_plus_y_inverse,x)),
inference(step,[status(thm)],[t3585,t319]) ).
cnf(t23771,plain,
x_inverse_plus_y_inverse = add(x_inverse_plus_y_inverse,inverse(x)),
inference(step,[status(thm)],[t23770,t2660]) ).
cnf(t3593,plain,
add(x_inverse_plus_y_inverse,inverse(x)) = x_inverse_plus_y_inverse,
inference(orient,[status(thm)],[t23771]) ).
cnf(t3596,plain,
add(x_inverse_plus_y_inverse,multiply(inverse(x),X1)) = multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,X1)),
inference(cp,[status(thm)],[t275,t3593]) ).
cnf(t4059,plain,
add(x_inverse_plus_y_inverse,multiply(inverse(x),X1)) = multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,X1)),
inference(orient,[status(thm)],[t3596]) ).
cnf(t4061,plain,
multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,x)) = add(x_inverse_plus_y_inverse,additive_identity),
inference(cp,[status(thm)],[t4059,t416]) ).
cnf(t23794,plain,
multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,x)) = x_inverse_plus_y_inverse,
inference(step,[status(thm)],[t4061,t256]) ).
cnf(t4078,plain,
multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,x)) = x_inverse_plus_y_inverse,
inference(orient,[status(thm)],[t23794]) ).
cnf(t4080,plain,
add(add(x_inverse_plus_y_inverse,x),inverse(x_inverse_plus_y_inverse)) = add(inverse(x_inverse_plus_y_inverse),x_inverse_plus_y_inverse),
inference(cp,[status(thm)],[t2614,t4078]) ).
cnf(t23796,plain,
add(inverse(x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,x)) = add(inverse(x_inverse_plus_y_inverse),x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t4080,t265]) ).
cnf(t23797,plain,
add(inverse(x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,x)) = add(x_inverse_plus_y_inverse,inverse(x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t23796,t265]) ).
cnf(t23798,plain,
add(inverse(x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,x)) = multiplicative_identity,
inference(step,[status(thm)],[t23797,t266]) ).
cnf(t4140,plain,
add(inverse(x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,x)) = multiplicative_identity,
inference(orient,[status(thm)],[t23798]) ).
cnf(t4142,plain,
add(add(x_inverse_plus_y_inverse,x),multiply(X1,inverse(x_inverse_plus_y_inverse))) = multiply(add(add(x_inverse_plus_y_inverse,x),X1),multiplicative_identity),
inference(cp,[status(thm)],[t3664,t4140]) ).
cnf(t24241,plain,
add(add(x_inverse_plus_y_inverse,x),multiply(X1,inverse(x_inverse_plus_y_inverse))) = add(add(x_inverse_plus_y_inverse,x),X1),
inference(step,[status(thm)],[t4142,t258]) ).
cnf(t20946,plain,
add(add(x_inverse_plus_y_inverse,x),multiply(X1,inverse(x_inverse_plus_y_inverse))) = add(add(x_inverse_plus_y_inverse,x),X1),
inference(orient,[status(thm)],[t24241]) ).
cnf(t20951,plain,
add(add(x_inverse_plus_y_inverse,x),x_inverse_plus_y_inverse) = add(add(x_inverse_plus_y_inverse,x),additive_identity),
inference(cp,[status(thm)],[t20946,t412]) ).
cnf(t24243,plain,
add(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,x)) = add(add(x_inverse_plus_y_inverse,x),additive_identity),
inference(step,[status(thm)],[t20951,t265]) ).
cnf(t24244,plain,
add(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,x)) = add(x_inverse_plus_y_inverse,x),
inference(step,[status(thm)],[t24243,t256]) ).
cnf(t20998,plain,
add(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,x)) = add(x_inverse_plus_y_inverse,x),
inference(orient,[status(thm)],[t24244]) ).
cnf(t21005,plain,
add(x_inverse_plus_y_inverse,multiply(add(x_inverse_plus_y_inverse,x),X1)) = multiply(add(x_inverse_plus_y_inverse,x),add(X1,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t3664,t20998]) ).
cnf(t24254,plain,
add(x_inverse_plus_y_inverse,multiply(add(x_inverse_plus_y_inverse,x),X1)) = add(x_inverse_plus_y_inverse,multiply(x,X1)),
inference(step,[status(thm)],[t21005,t3664]) ).
cnf(t21284,plain,
add(x_inverse_plus_y_inverse,multiply(add(x_inverse_plus_y_inverse,x),X1)) = add(x_inverse_plus_y_inverse,multiply(x,X1)),
inference(orient,[status(thm)],[t24254]) ).
cnf(t21292,plain,
add(x_inverse_plus_y_inverse,multiply(x,add(x,X1))) = add(x_inverse_plus_y_inverse,add(x,multiply(x_inverse_plus_y_inverse,X1))),
inference(cp,[status(thm)],[t21284,t4534]) ).
cnf(t22944,plain,
add(x_inverse_plus_y_inverse,add(x,multiply(x_inverse_plus_y_inverse,X1))) = add(x_inverse_plus_y_inverse,multiply(x,add(x,X1))),
inference(orient,[status(thm)],[t21292]) ).
cnf(t189,plain,
sum(inverse(x),additive_identity,multiply(x_inverse_plus_y_inverse,add(inverse(x),y))) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi23,hi0,hi18,hi1]) ).
cnf(t23658,plain,
sum(inverse(x),additive_identity,multiply(x_inverse_plus_y_inverse,add(y,inverse(x)))) = true,
inference(step,[status(thm)],[t189,t265]) ).
cnf(t566,plain,
sum(inverse(x),additive_identity,multiply(x_inverse_plus_y_inverse,add(y,inverse(x)))) = true,
inference(orient,[status(thm)],[t23658]) ).
cnf(t2972,plain,
multiply(x_inverse_plus_y_inverse,add(y,inverse(x))) = ifeq(true,true,inverse(x),multiply(x_inverse_plus_y_inverse,add(y,inverse(x)))),
inference(cp,[status(thm)],[t2968,t566]) ).
cnf(t23748,plain,
multiply(x_inverse_plus_y_inverse,add(y,inverse(x))) = inverse(x),
inference(step,[status(thm)],[t2972,t260]) ).
cnf(t3157,plain,
multiply(x_inverse_plus_y_inverse,add(y,inverse(x))) = inverse(x),
inference(orient,[status(thm)],[t23748]) ).
cnf(t22975,plain,
add(x_inverse_plus_y_inverse,multiply(x,add(x,add(y,inverse(x))))) = add(x_inverse_plus_y_inverse,add(x,inverse(x))),
inference(cp,[status(thm)],[t22944,t3157]) ).
cnf(t2193,plain,
add(X1,X1) = add(X1,additive_identity),
inference(cp,[status(thm)],[t2190,t416]) ).
cnf(t23682,plain,
add(X1,X1) = X1,
inference(step,[status(thm)],[t2193,t256]) ).
cnf(t2218,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t23682]) ).
cnf(t2224,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(cp,[status(thm)],[t275,t2218]) ).
cnf(t2402,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(orient,[status(thm)],[t2224]) ).
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(t230,plain,
sum(x_times_y,additive_identity,add(additive_identity,multiply(x,add(inverse(x),y)))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi22,hi19,h1,h14]) ).
cnf(t23673,plain,
sum(x_times_y,additive_identity,multiply(x,add(inverse(x),y))) = true,
inference(step,[status(thm)],[t230,t257]) ).
cnf(t23674,plain,
sum(x_times_y,additive_identity,multiply(x,add(y,inverse(x)))) = true,
inference(step,[status(thm)],[t23673,t265]) ).
cnf(t632,plain,
sum(x_times_y,additive_identity,multiply(x,add(y,inverse(x)))) = true,
inference(orient,[status(thm)],[t23674]) ).
cnf(t2969,plain,
multiply(x,add(y,inverse(x))) = ifeq(true,true,x_times_y,multiply(x,add(y,inverse(x)))),
inference(cp,[status(thm)],[t2968,t632]) ).
cnf(t23743,plain,
multiply(x,add(y,inverse(x))) = x_times_y,
inference(step,[status(thm)],[t2969,t260]) ).
cnf(t3039,plain,
multiply(x,add(y,inverse(x))) = x_times_y,
inference(orient,[status(thm)],[t23743]) ).
cnf(t3043,plain,
multiply(x,add(x,add(y,inverse(x)))) = add(x,x_times_y),
inference(cp,[status(thm)],[t2402,t3039]) ).
cnf(t23884,plain,
multiply(x,add(x,add(y,inverse(x)))) = add(x_times_y,x),
inference(step,[status(thm)],[t3043,t265]) ).
cnf(t6072,plain,
multiply(x,add(x,add(y,inverse(x)))) = add(x_times_y,x),
inference(orient,[status(thm)],[t23884]) ).
cnf(t24282,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x)) = add(x_inverse_plus_y_inverse,add(x,inverse(x))),
inference(step,[status(thm)],[t22975,t6072]) ).
cnf(t21004,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(x_inverse_plus_y_inverse,x))) = multiply(add(X1,x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,x)),
inference(cp,[status(thm)],[t4534,t20998]) ).
cnf(t24249,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(x_inverse_plus_y_inverse,x))) = add(x_inverse_plus_y_inverse,multiply(X1,x)),
inference(step,[status(thm)],[t21004,t4534]) ).
cnf(t21117,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(x_inverse_plus_y_inverse,x))) = add(x_inverse_plus_y_inverse,multiply(X1,x)),
inference(orient,[status(thm)],[t24249]) ).
cnf(t21128,plain,
add(x_inverse_plus_y_inverse,multiply(add(X1,x),x)) = add(x_inverse_plus_y_inverse,add(x,multiply(X1,x_inverse_plus_y_inverse))),
inference(cp,[status(thm)],[t21117,t268]) ).
cnf(t22658,plain,
add(x_inverse_plus_y_inverse,add(x,multiply(X1,x_inverse_plus_y_inverse))) = add(x_inverse_plus_y_inverse,multiply(add(X1,x),x)),
inference(orient,[status(thm)],[t21128]) ).
cnf(t154,plain,
sum(multiply(y,inverse(x)),additive_identity,multiply(y,x_inverse_plus_y_inverse)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi1,hi19,hi23,hi1]) ).
cnf(t593,plain,
sum(multiply(y,inverse(x)),additive_identity,multiply(y,x_inverse_plus_y_inverse)) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(t2970,plain,
multiply(y,x_inverse_plus_y_inverse) = ifeq(true,true,multiply(y,inverse(x)),multiply(y,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t2968,t593]) ).
cnf(t23728,plain,
multiply(y,x_inverse_plus_y_inverse) = multiply(y,inverse(x)),
inference(step,[status(thm)],[t2970,t260]) ).
cnf(t2982,plain,
multiply(y,inverse(x)) = multiply(y,x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t23728]) ).
cnf(t2983,plain,
add(y,inverse(inverse(x))) = add(inverse(inverse(x)),multiply(y,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t2660,t2982]) ).
cnf(t23735,plain,
add(y,x) = add(inverse(inverse(x)),multiply(y,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t2983,t2641]) ).
cnf(t23736,plain,
add(y,x) = add(multiply(y,x_inverse_plus_y_inverse),inverse(inverse(x))),
inference(step,[status(thm)],[t23735,t265]) ).
cnf(t23737,plain,
add(y,x) = add(multiply(y,x_inverse_plus_y_inverse),x),
inference(step,[status(thm)],[t23736,t2641]) ).
cnf(t23738,plain,
add(y,x) = add(x,multiply(y,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t23737,t265]) ).
cnf(t3015,plain,
add(x,multiply(y,x_inverse_plus_y_inverse)) = add(y,x),
inference(orient,[status(thm)],[t23738]) ).
cnf(t22663,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x),x)) = add(x_inverse_plus_y_inverse,add(y,x)),
inference(cp,[status(thm)],[t22658,t3015]) ).
cnf(t2984,plain,
add(inverse(x),inverse(y)) = add(inverse(y),multiply(y,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t2614,t2982]) ).
cnf(t23744,plain,
add(inverse(y),inverse(x)) = add(inverse(y),multiply(y,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t2984,t265]) ).
cnf(t23745,plain,
x_inverse_plus_y_inverse = add(inverse(y),multiply(y,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t23744,t319]) ).
cnf(t23746,plain,
x_inverse_plus_y_inverse = add(x_inverse_plus_y_inverse,inverse(y)),
inference(step,[status(thm)],[t23745,t2614]) ).
cnf(t3092,plain,
add(x_inverse_plus_y_inverse,inverse(y)) = x_inverse_plus_y_inverse,
inference(orient,[status(thm)],[t23746]) ).
cnf(t3095,plain,
add(x_inverse_plus_y_inverse,multiply(inverse(y),X1)) = multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,X1)),
inference(cp,[status(thm)],[t275,t3092]) ).
cnf(t3392,plain,
add(x_inverse_plus_y_inverse,multiply(inverse(y),X1)) = multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,X1)),
inference(orient,[status(thm)],[t3095]) ).
cnf(t3394,plain,
multiply(x_inverse_plus_y_inverse,add(x_inverse_plus_y_inverse,y)) = add(x_inverse_plus_y_inverse,additive_identity),
inference(cp,[status(thm)],[t3392,t416]) ).
cnf(t23755,plain,
multiply(x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)) = add(x_inverse_plus_y_inverse,additive_identity),
inference(step,[status(thm)],[t3394,t265]) ).
cnf(t23756,plain,
multiply(x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)) = x_inverse_plus_y_inverse,
inference(step,[status(thm)],[t23755,t256]) ).
cnf(t3409,plain,
multiply(x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)) = x_inverse_plus_y_inverse,
inference(orient,[status(thm)],[t23756]) ).
cnf(t3411,plain,
add(add(y,x_inverse_plus_y_inverse),inverse(x_inverse_plus_y_inverse)) = add(inverse(x_inverse_plus_y_inverse),x_inverse_plus_y_inverse),
inference(cp,[status(thm)],[t2614,t3409]) ).
cnf(t23758,plain,
add(inverse(x_inverse_plus_y_inverse),add(y,x_inverse_plus_y_inverse)) = add(inverse(x_inverse_plus_y_inverse),x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t3411,t265]) ).
cnf(t23759,plain,
add(inverse(x_inverse_plus_y_inverse),add(y,x_inverse_plus_y_inverse)) = add(x_inverse_plus_y_inverse,inverse(x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t23758,t265]) ).
cnf(t23760,plain,
add(inverse(x_inverse_plus_y_inverse),add(y,x_inverse_plus_y_inverse)) = multiplicative_identity,
inference(step,[status(thm)],[t23759,t266]) ).
cnf(t3471,plain,
add(inverse(x_inverse_plus_y_inverse),add(y,x_inverse_plus_y_inverse)) = multiplicative_identity,
inference(orient,[status(thm)],[t23760]) ).
cnf(t3476,plain,
add(add(y,x_inverse_plus_y_inverse),multiply(inverse(x_inverse_plus_y_inverse),X1)) = multiply(multiplicative_identity,add(X1,add(y,x_inverse_plus_y_inverse))),
inference(cp,[status(thm)],[t268,t3471]) ).
cnf(t24170,plain,
add(add(y,x_inverse_plus_y_inverse),multiply(inverse(x_inverse_plus_y_inverse),X1)) = add(X1,add(y,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t3476,t259]) ).
cnf(t18095,plain,
add(add(y,x_inverse_plus_y_inverse),multiply(inverse(x_inverse_plus_y_inverse),X1)) = add(X1,add(y,x_inverse_plus_y_inverse)),
inference(orient,[status(thm)],[t24170]) ).
cnf(t18104,plain,
add(x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)) = add(add(y,x_inverse_plus_y_inverse),additive_identity),
inference(cp,[status(thm)],[t18095,t416]) ).
cnf(t24171,plain,
add(x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)) = add(y,x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t18104,t256]) ).
cnf(t18148,plain,
add(x_inverse_plus_y_inverse,add(y,x_inverse_plus_y_inverse)) = add(y,x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t24171]) ).
cnf(t18154,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_inverse_plus_y_inverse))) = multiply(add(X1,x_inverse_plus_y_inverse),add(y,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t4534,t18148]) ).
cnf(t24178,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_inverse_plus_y_inverse))) = add(x_inverse_plus_y_inverse,multiply(X1,y)),
inference(step,[status(thm)],[t18154,t268]) ).
cnf(t18265,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_inverse_plus_y_inverse))) = add(x_inverse_plus_y_inverse,multiply(X1,y)),
inference(orient,[status(thm)],[t24178]) ).
cnf(t18284,plain,
add(x_inverse_plus_y_inverse,multiply(add(X1,y),y)) = add(x_inverse_plus_y_inverse,add(y,multiply(X1,x_inverse_plus_y_inverse))),
inference(cp,[status(thm)],[t18265,t4534]) ).
cnf(t19465,plain,
add(x_inverse_plus_y_inverse,add(y,multiply(X1,x_inverse_plus_y_inverse))) = add(x_inverse_plus_y_inverse,multiply(add(X1,y),y)),
inference(orient,[status(thm)],[t18284]) ).
cnf(t146,plain,
sum(additive_identity,multiply(x,inverse(y)),multiply(x,x_inverse_plus_y_inverse)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi19,hi1,hi23,hi1]) ).
cnf(t608,plain,
sum(additive_identity,multiply(x,inverse(y)),multiply(x,x_inverse_plus_y_inverse)) = true,
inference(orient,[status(thm)],[t146]) ).
cnf(t3575,plain,
multiply(x,x_inverse_plus_y_inverse) = ifeq(true,true,multiply(x,inverse(y)),multiply(x,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t3573,t608]) ).
cnf(t23772,plain,
multiply(x,x_inverse_plus_y_inverse) = multiply(x,inverse(y)),
inference(step,[status(thm)],[t3575,t260]) ).
cnf(t3605,plain,
multiply(x,inverse(y)) = multiply(x,x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t23772]) ).
cnf(t3606,plain,
add(x,inverse(inverse(y))) = add(inverse(inverse(y)),multiply(x,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t2660,t3605]) ).
cnf(t23782,plain,
add(x,y) = add(inverse(inverse(y)),multiply(x,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t3606,t2641]) ).
cnf(t23783,plain,
add(y,x) = add(inverse(inverse(y)),multiply(x,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t23782,t265]) ).
cnf(t23784,plain,
add(y,x) = add(multiply(x,x_inverse_plus_y_inverse),inverse(inverse(y))),
inference(step,[status(thm)],[t23783,t265]) ).
cnf(t23785,plain,
add(y,x) = add(multiply(x,x_inverse_plus_y_inverse),y),
inference(step,[status(thm)],[t23784,t2641]) ).
cnf(t23786,plain,
add(y,x) = add(y,multiply(x,x_inverse_plus_y_inverse)),
inference(step,[status(thm)],[t23785,t265]) ).
cnf(t3770,plain,
add(y,multiply(x,x_inverse_plus_y_inverse)) = add(y,x),
inference(orient,[status(thm)],[t23786]) ).
cnf(t19472,plain,
add(x_inverse_plus_y_inverse,multiply(add(x,y),y)) = add(x_inverse_plus_y_inverse,add(y,x)),
inference(cp,[status(thm)],[t19465,t3770]) ).
cnf(t24204,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x),y)) = add(x_inverse_plus_y_inverse,add(y,x)),
inference(step,[status(thm)],[t19472,t265]) ).
cnf(t2225,plain,
add(X1,multiply(X2,X1)) = multiply(add(X1,X2),X1),
inference(cp,[status(thm)],[t275,t2218]) ).
cnf(t2429,plain,
add(X1,multiply(X2,X1)) = multiply(add(X1,X2),X1),
inference(orient,[status(thm)],[t2225]) ).
cnf(t2432,plain,
multiply(add(y,x),y) = add(y,x_times_y),
inference(cp,[status(thm)],[t2429,t420]) ).
cnf(t2453,plain,
multiply(add(y,x),y) = add(y,x_times_y),
inference(orient,[status(thm)],[t2432]) ).
cnf(t24205,plain,
add(x_inverse_plus_y_inverse,add(y,x_times_y)) = add(x_inverse_plus_y_inverse,add(y,x)),
inference(step,[status(thm)],[t24204,t2453]) ).
cnf(t19536,plain,
add(x_inverse_plus_y_inverse,add(y,x)) = add(x_inverse_plus_y_inverse,add(y,x_times_y)),
inference(orient,[status(thm)],[t24205]) ).
cnf(t19539,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x),X1)) = multiply(add(x_inverse_plus_y_inverse,add(y,x_times_y)),add(X1,x_inverse_plus_y_inverse)),
inference(cp,[status(thm)],[t3664,t19536]) ).
cnf(t24223,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x),X1)) = add(x_inverse_plus_y_inverse,multiply(add(y,x_times_y),X1)),
inference(step,[status(thm)],[t19539,t3664]) ).
cnf(t20257,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x),X1)) = add(x_inverse_plus_y_inverse,multiply(add(y,x_times_y),X1)),
inference(orient,[status(thm)],[t24223]) ).
cnf(t24272,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x_times_y),x)) = add(x_inverse_plus_y_inverse,add(y,x)),
inference(step,[status(thm)],[t22663,t20257]) ).
cnf(t14,plain,
product(x,y,x_times_y) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t475,plain,
product(x,y,x_times_y) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t476,plain,
X1 = ifeq(true,true,ifeq(product(x,y,X1),true,x_times_y,X1),X1),
inference(cp,[status(thm)],[t261,t475]) ).
cnf(t23719,plain,
X1 = ifeq(product(x,y,X1),true,x_times_y,X1),
inference(step,[status(thm)],[t476,t260]) ).
cnf(t2872,plain,
ifeq(product(x,y,X1),true,x_times_y,X1) = X1,
inference(orient,[status(thm)],[t23719]) ).
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(t212,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t635,plain,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t212]) ).
cnf(t35,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t423,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t636,plain,
true = ifeq(true,true,product(X1,X2,multiply(X2,X1)),true),
inference(cp,[status(thm)],[t635,t423]) ).
cnf(t23678,plain,
true = product(X1,X2,multiply(X2,X1)),
inference(step,[status(thm)],[t636,t260]) ).
cnf(t2021,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(orient,[status(thm)],[t23678]) ).
cnf(t2873,plain,
multiply(y,x) = ifeq(true,true,x_times_y,multiply(y,x)),
inference(cp,[status(thm)],[t2872,t2021]) ).
cnf(t23720,plain,
multiply(y,x) = x_times_y,
inference(step,[status(thm)],[t2873,t260]) ).
cnf(t2874,plain,
multiply(y,x) = x_times_y,
inference(orient,[status(thm)],[t23720]) ).
cnf(t2877,plain,
multiply(add(x,y),x) = add(x,x_times_y),
inference(cp,[status(thm)],[t2429,t2874]) ).
cnf(t23721,plain,
multiply(add(y,x),x) = add(x,x_times_y),
inference(step,[status(thm)],[t2877,t265]) ).
cnf(t23722,plain,
multiply(add(y,x),x) = add(x_times_y,x),
inference(step,[status(thm)],[t23721,t265]) ).
cnf(t2879,plain,
multiply(add(y,x),x) = add(x_times_y,x),
inference(orient,[status(thm)],[t23722]) ).
cnf(t20267,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x_times_y),x)) = add(x_inverse_plus_y_inverse,add(x_times_y,x)),
inference(cp,[status(thm)],[t20257,t2879]) ).
cnf(t20348,plain,
add(x_inverse_plus_y_inverse,multiply(add(y,x_times_y),x)) = add(x_inverse_plus_y_inverse,add(x_times_y,x)),
inference(orient,[status(thm)],[t20267]) ).
cnf(t24273,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x)) = add(x_inverse_plus_y_inverse,add(y,x)),
inference(step,[status(thm)],[t24272,t20348]) ).
cnf(t24274,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x)) = add(x_inverse_plus_y_inverse,add(y,x_times_y)),
inference(step,[status(thm)],[t24273,t19536]) ).
cnf(t22729,plain,
add(x_inverse_plus_y_inverse,add(x_times_y,x)) = add(x_inverse_plus_y_inverse,add(y,x_times_y)),
inference(orient,[status(thm)],[t24274]) ).
cnf(t24283,plain,
add(x_inverse_plus_y_inverse,add(y,x_times_y)) = add(x_inverse_plus_y_inverse,add(x,inverse(x))),
inference(step,[status(thm)],[t24282,t22729]) ).
cnf(t24284,plain,
add(x_inverse_plus_y_inverse,add(y,x_times_y)) = add(x_inverse_plus_y_inverse,multiplicative_identity),
inference(step,[status(thm)],[t24283,t266]) ).
cnf(t2196,plain,
add(X1,multiplicative_identity) = add(X1,inverse(X1)),
inference(cp,[status(thm)],[t2190,t258]) ).
cnf(t23683,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(step,[status(thm)],[t2196,t266]) ).
cnf(t2233,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(orient,[status(thm)],[t23683]) ).
cnf(t24285,plain,
add(x_inverse_plus_y_inverse,add(y,x_times_y)) = multiplicative_identity,
inference(step,[status(thm)],[t24284,t2233]) ).
cnf(t23015,plain,
add(x_inverse_plus_y_inverse,add(y,x_times_y)) = multiplicative_identity,
inference(orient,[status(thm)],[t24285]) ).
cnf(t23031,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_times_y))) = multiply(add(X1,x_inverse_plus_y_inverse),multiplicative_identity),
inference(cp,[status(thm)],[t4534,t23015]) ).
cnf(t24299,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_times_y))) = add(X1,x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t23031,t258]) ).
cnf(t23148,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_times_y))) = add(X1,x_inverse_plus_y_inverse),
inference(orient,[status(thm)],[t24299]) ).
cnf(t24304,plain,
add(x_times_y,x_inverse_plus_y_inverse) = add(y,x_inverse_plus_y_inverse),
inference(step,[status(thm)],[t16094,t23148]) ).
cnf(t23219,plain,
add(x_times_y,x_inverse_plus_y_inverse) = add(y,x_inverse_plus_y_inverse),
inference(rw,[status(thm)],[t24304]) ).
cnf(t19538,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x))) = multiply(add(X1,x_inverse_plus_y_inverse),add(x_inverse_plus_y_inverse,add(y,x_times_y))),
inference(cp,[status(thm)],[t4534,t19536]) ).
cnf(t24222,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x))) = add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_times_y))),
inference(step,[status(thm)],[t19538,t4534]) ).
cnf(t20140,plain,
add(x_inverse_plus_y_inverse,multiply(X1,add(y,x))) = add(x_inverse_plus_y_inverse,multiply(X1,add(y,x_times_y))),
inference(orient,[status(thm)],[t24222]) ).
cnf(t2878,plain,
multiply(y,add(y,x)) = add(y,x_times_y),
inference(cp,[status(thm)],[t2402,t2874]) ).
cnf(t2886,plain,
multiply(y,add(y,x)) = add(y,x_times_y),
inference(orient,[status(thm)],[t2878]) ).
cnf(t20150,plain,
add(x_inverse_plus_y_inverse,multiply(y,add(y,x_times_y))) = add(x_inverse_plus_y_inverse,add(y,x_times_y)),
inference(cp,[status(thm)],[t20140,t2886]) ).
cnf(t20192,plain,
add(x_inverse_plus_y_inverse,multiply(y,add(y,x_times_y))) = add(x_inverse_plus_y_inverse,add(y,x_times_y)),
inference(orient,[status(thm)],[t20150]) ).
cnf(t24288,plain,
add(x_inverse_plus_y_inverse,multiply(y,add(y,x_times_y))) = multiplicative_identity,
inference(step,[status(thm)],[t20192,t23015]) ).
cnf(t23018,plain,
add(x_inverse_plus_y_inverse,multiply(y,add(y,x_times_y))) = multiplicative_identity,
inference(orient,[status(thm)],[t24288]) ).
cnf(t24303,plain,
add(y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(step,[status(thm)],[t23018,t23148]) ).
cnf(t23218,plain,
add(y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(rw,[status(thm)],[t24303]) ).
cnf(t23278,plain,
add(y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(orient,[status(thm)],[t23218]) ).
cnf(t24400,plain,
add(x_times_y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(step,[status(thm)],[t23219,t23278]) ).
cnf(t23333,plain,
add(x_times_y,x_inverse_plus_y_inverse) = multiplicative_identity,
inference(orient,[status(thm)],[t24400]) ).
cnf(t24405,plain,
multiply(inverse(x_inverse_plus_y_inverse),multiplicative_identity) = x_times_y,
inference(step,[status(thm)],[t14518,t23333]) ).
cnf(t24406,plain,
inverse(x_inverse_plus_y_inverse) = x_times_y,
inference(step,[status(thm)],[t24405,t258]) ).
cnf(t23366,plain,
inverse(x_inverse_plus_y_inverse) = x_times_y,
inference(rw,[status(thm)],[t24406]) ).
cnf(t23383,plain,
inverse(x_inverse_plus_y_inverse) = x_times_y,
inference(orient,[status(thm)],[t23366]) ).
cnf(t23396,plain,
x_inverse_plus_y_inverse = inverse(x_times_y),
inference(cp,[status(thm)],[t2641,t23383]) ).
cnf(t23508,plain,
inverse(x_times_y) = x_inverse_plus_y_inverse,
inference(orient,[status(thm)],[t23396]) ).
cnf(f24,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f24_nnf,plain,
inverse(x_times_y) != x_inverse_plus_y_inverse,
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
inverse(x_times_y) != x_inverse_plus_y_inverse,
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
inverse(x_times_y) != x_inverse_plus_y_inverse,
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(g0_0,plain,
x_inverse_plus_y_inverse != x_inverse_plus_y_inverse,
inference(rw,[status(thm)],[goal_0,t23508]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO015-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 06:32:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 73.24/9.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.24/9.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------