%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:37:25 PM UTC 2026
% Result : Unsatisfiable 30.41s 4.39s
% Output : Proof 30.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 21
% Syntax : Number of formulae : 292 ( 244 unt; 0 def)
% Number of atoms : 432 ( 220 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 286 ( 146 ~; 140 |; 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 : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 608 ( 10 sgn 152 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f2_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t46,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t677,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(f10,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f10_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X0,X4,X5),true,product(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h5,plain,
product(multiply(V0,V1),V2,multiply(V0,multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi2,hi2,hi2]) ).
cnf(f16,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f16_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f19,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f19_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
product(X0,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t135,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(hyper_resolution,[status(thm)],[hi16,hi19,h5]) ).
cnf(t432,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(orient,[status(thm)],[t135]) ).
cnf(f12,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f12_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f1,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f1_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f3,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f3_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h14,plain,
product(V0,V1,add(multiply(V0,V1),multiply(V0,additive_identity))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2,hi2,hi1,hi3]) ).
cnf(f9,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f9_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X2,X3,X5),true,product(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h6,plain,
product(V0,multiply(V1,V2),multiply(multiply(V0,V1),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi2,hi2,hi2]) ).
cnf(t233,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X1,additive_identity)) = multiply(multiply(X1,X2),X3),
inference(hyper_resolution,[status(thm)],[hi16,h6,h14]) ).
cnf(f6,axiom,
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f6_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X2,X3,X5),true,sum(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h31,plain,
sum(V0,V1,add(add(V0,V1),additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,hi1,hi3]) ).
cnf(f11,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f11_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(product(X0,X5,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h16,plain,
sum(multiply(V0,V1),multiply(V0,V2),multiply(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi3,hi2]) ).
cnf(f15,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f15_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t225,plain,
add(add(multiply(X1,X2),multiply(X1,X3)),additive_identity) = multiply(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h16,h31]) ).
cnf(f7,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f7_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X0,X4,X5),true,sum(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(t121,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t335,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t121]) ).
cnf(t5306,plain,
add(multiply(X1,X2),add(multiply(X1,X3),additive_identity)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t225,t335]) ).
cnf(f8,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h17,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3]) ).
cnf(t120,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,h17,h18]) ).
cnf(t309,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(orient,[status(thm)],[t120]) ).
cnf(t5307,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t5306,t309]) ).
cnf(h27,plain,
sum(add(V0,additive_identity),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi1,hi1]) ).
cnf(f0,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f0_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h24,plain,
sum(V0,additive_identity,add(additive_identity,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,hi1,hi3]) ).
cnf(f18,axiom,
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
fof(f18_nnf,plain,
! [X,Y,Z,W] :
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z,W] :
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X2),true,X0,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t23,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi18,h24,h27]) ).
cnf(t1,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi18,hi1,hi3]) ).
cnf(t257,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t5297,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t23,t257]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t5297]) ).
cnf(t5308,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t5307,t258]) ).
cnf(t394,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t5308]) ).
cnf(t5310,plain,
multiply(X1,add(multiply(X2,X3),additive_identity)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t233,t394]) ).
cnf(t5311,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t5310,t257]) ).
cnf(t417,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t5311]) ).
cnf(f14,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f14_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h11,plain,
product(V0,V1,add(multiply(additive_identity,V1),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi0,hi3]) ).
cnf(f20,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f20_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t73,plain,
add(multiply(additive_identity,b),multiply(a,b)) = c,
inference(hyper_resolution,[status(thm)],[hi16,hi20,h11]) ).
cnf(f13,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f13_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(product(X5,X1,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h12,plain,
sum(multiply(V0,V1),multiply(V2,V1),multiply(add(V0,V2),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi3,hi2]) ).
cnf(t226,plain,
add(add(multiply(X1,X2),multiply(X3,X2)),additive_identity) = multiply(add(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi15,h12,h31]) ).
cnf(t5303,plain,
add(multiply(X1,X2),add(multiply(X3,X2),additive_identity)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t226,t335]) ).
cnf(t5304,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t5303,t309]) ).
cnf(t5305,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t5304,t258]) ).
cnf(t383,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t5305]) ).
cnf(t5312,plain,
multiply(add(additive_identity,a),b) = c,
inference(step,[status(thm)],[t73,t383]) ).
cnf(t5313,plain,
multiply(a,b) = c,
inference(step,[status(thm)],[t5312,t258]) ).
cnf(t422,plain,
multiply(a,b) = c,
inference(orient,[status(thm)],[t5313]) ).
cnf(t423,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(cp,[status(thm)],[t417,t422]) ).
cnf(t1613,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(orient,[status(thm)],[t423]) ).
cnf(t1629,plain,
multiply(b,a) = multiply(b,multiply(c,a)),
inference(cp,[status(thm)],[t432,t1613]) ).
cnf(t1671,plain,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(orient,[status(thm)],[t1629]) ).
cnf(t5,plain,
multiply(X1,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi2,hi19]) ).
cnf(t263,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t397,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t394,t263]) ).
cnf(t1851,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(orient,[status(thm)],[t397]) ).
cnf(t419,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t417,t263]) ).
cnf(t1580,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t419]) ).
cnf(t1590,plain,
multiply(X1,add(multiply(X1,X2),X3)) = add(multiply(X1,X2),multiply(X1,X3)),
inference(cp,[status(thm)],[t394,t1580]) ).
cnf(t5442,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t1590,t394]) ).
cnf(t3683,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t5442]) ).
cnf(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi3,hi3]) ).
cnf(f5,axiom,
sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
sum(X0,additive_inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t38,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(t5302,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t38,t258]) ).
cnf(t372,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5302]) ).
cnf(t3690,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = multiply(X1,additive_identity),
inference(cp,[status(thm)],[t3683,t372]) ).
cnf(h29,plain,
sum(add(additive_identity,additive_identity),V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi0,hi0]) ).
cnf(h4,plain,
sum(multiply(V0,additive_identity),multiply(V0,V1),multiply(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi0,hi2]) ).
cnf(t31,plain,
multiply(X1,additive_identity) = add(additive_identity,additive_identity),
inference(hyper_resolution,[status(thm)],[hi18,h4,h29]) ).
cnf(t5314,plain,
multiply(X1,additive_identity) = additive_identity,
inference(step,[status(thm)],[t31,t258]) ).
cnf(t428,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t5314]) ).
cnf(t5443,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(step,[status(thm)],[t3690,t428]) ).
cnf(t3760,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t5443]) ).
cnf(t386,plain,
multiply(add(X1,X2),X1) = add(X1,multiply(X2,X1)),
inference(cp,[status(thm)],[t383,t263]) ).
cnf(t1741,plain,
add(X1,multiply(X2,X1)) = multiply(add(X1,X2),X1),
inference(orient,[status(thm)],[t386]) ).
cnf(t1753,plain,
multiply(add(b,a),b) = add(b,c),
inference(cp,[status(thm)],[t1741,t422]) ).
cnf(t20,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h17]) ).
cnf(t284,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t20]) ).
cnf(t5352,plain,
multiply(add(b,a),b) = add(c,b),
inference(step,[status(thm)],[t1753,t284]) ).
cnf(t1822,plain,
multiply(add(b,a),b) = add(c,b),
inference(orient,[status(thm)],[t5352]) ).
cnf(t3770,plain,
additive_identity = multiply(add(b,a),add(b,additive_inverse(add(c,b)))),
inference(cp,[status(thm)],[t3760,t1822]) ).
cnf(t375,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t335,t372]) ).
cnf(t5348,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t375,t258]) ).
cnf(t1678,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t5348]) ).
cnf(t80,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t350,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t80]) ).
cnf(t1680,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = add(X2,additive_identity),
inference(cp,[status(thm)],[t1678,t350]) ).
cnf(t5386,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(step,[status(thm)],[t1680,t257]) ).
cnf(t2224,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t5386]) ).
cnf(f4,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f4_nnf,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : sum(additive_inverse(X),X,additive_identity),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
sum(additive_inverse(X0),X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t4,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi18,hi4,hi5]) ).
cnf(t283,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t2231,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t2224,t283]) ).
cnf(t2246,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t2231]) ).
cnf(t5444,plain,
additive_identity = multiply(add(b,a),additive_inverse(c)),
inference(step,[status(thm)],[t3770,t2246]) ).
cnf(t3803,plain,
multiply(add(b,a),additive_inverse(c)) = additive_identity,
inference(orient,[status(thm)],[t5444]) ).
cnf(t3807,plain,
multiply(add(b,a),multiply(additive_inverse(c),X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t417,t3803]) ).
cnf(h2,plain,
sum(multiply(additive_identity,V0),multiply(V1,V0),multiply(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi0,hi2]) ).
cnf(t32,plain,
multiply(additive_identity,X1) = add(additive_identity,additive_identity),
inference(hyper_resolution,[status(thm)],[hi18,h2,h29]) ).
cnf(t5315,plain,
multiply(additive_identity,X1) = additive_identity,
inference(step,[status(thm)],[t32,t258]) ).
cnf(t430,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t5315]) ).
cnf(t5447,plain,
multiply(add(b,a),multiply(additive_inverse(c),X1)) = additive_identity,
inference(step,[status(thm)],[t3807,t430]) ).
cnf(t3884,plain,
multiply(add(b,a),multiply(additive_inverse(c),X1)) = additive_identity,
inference(orient,[status(thm)],[t5447]) ).
cnf(t3896,plain,
multiply(additive_inverse(c),add(b,a)) = multiply(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t432,t3884]) ).
cnf(t5448,plain,
multiply(additive_inverse(c),add(b,a)) = additive_identity,
inference(step,[status(thm)],[t3896,t428]) ).
cnf(t3897,plain,
multiply(additive_inverse(c),add(b,a)) = additive_identity,
inference(orient,[status(thm)],[t5448]) ).
cnf(t2255,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X2,X1))),
inference(cp,[status(thm)],[t2246,t284]) ).
cnf(t2314,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(orient,[status(thm)],[t2255]) ).
cnf(t1591,plain,
multiply(X1,add(X2,multiply(X1,X3))) = add(multiply(X1,X2),multiply(X1,X3)),
inference(cp,[status(thm)],[t394,t1580]) ).
cnf(t5458,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t1591,t394]) ).
cnf(t4063,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t5458]) ).
cnf(t4066,plain,
multiply(X1,add(X2,X2)) = multiply(X1,multiply(add(X2,X1),X2)),
inference(cp,[status(thm)],[t4063,t1741]) ).
cnf(t4836,plain,
multiply(X1,multiply(add(X2,X1),X2)) = multiply(X1,add(X2,X2)),
inference(orient,[status(thm)],[t4066]) ).
cnf(t4848,plain,
multiply(additive_inverse(X1),add(X1,X1)) = multiply(additive_inverse(X1),multiply(additive_identity,X1)),
inference(cp,[status(thm)],[t4836,t372]) ).
cnf(t5494,plain,
multiply(additive_inverse(X1),add(X1,X1)) = multiply(additive_inverse(X1),additive_identity),
inference(step,[status(thm)],[t4848,t430]) ).
cnf(t5495,plain,
multiply(additive_inverse(X1),add(X1,X1)) = additive_identity,
inference(step,[status(thm)],[t5494,t428]) ).
cnf(t4913,plain,
multiply(additive_inverse(X1),add(X1,X1)) = additive_identity,
inference(orient,[status(thm)],[t5495]) ).
cnf(t4916,plain,
additive_identity = multiply(X1,add(additive_inverse(X1),additive_inverse(X1))),
inference(cp,[status(thm)],[t4913,t283]) ).
cnf(t2266,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(cp,[status(thm)],[t1678,t2246]) ).
cnf(t2269,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(orient,[status(thm)],[t2266]) ).
cnf(t2272,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(cp,[status(thm)],[t2269,t283]) ).
cnf(t2296,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(orient,[status(thm)],[t2272]) ).
cnf(t5496,plain,
additive_identity = multiply(X1,additive_inverse(add(X1,X1))),
inference(step,[status(thm)],[t4916,t2296]) ).
cnf(t4932,plain,
multiply(X1,additive_inverse(add(X1,X1))) = additive_identity,
inference(orient,[status(thm)],[t5496]) ).
cnf(t4945,plain,
multiply(X1,add(X1,additive_inverse(add(X1,X1)))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1851,t4932]) ).
cnf(t5497,plain,
multiply(X1,additive_inverse(X1)) = add(X1,additive_identity),
inference(step,[status(thm)],[t4945,t2246]) ).
cnf(t5498,plain,
multiply(X1,additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t5497,t257]) ).
cnf(t4965,plain,
multiply(X1,additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t5498]) ).
cnf(t4976,plain,
multiply(X1,add(X1,additive_inverse(X1))) = add(X1,X1),
inference(cp,[status(thm)],[t1851,t4965]) ).
cnf(t5499,plain,
multiply(X1,additive_identity) = add(X1,X1),
inference(step,[status(thm)],[t4976,t372]) ).
cnf(t5500,plain,
additive_identity = add(X1,X1),
inference(step,[status(thm)],[t5499,t428]) ).
cnf(t4998,plain,
add(X1,X1) = additive_identity,
inference(orient,[status(thm)],[t5500]) ).
cnf(t5029,plain,
additive_inverse(X1) = add(X1,additive_inverse(additive_identity)),
inference(cp,[status(thm)],[t2314,t4998]) ).
cnf(t11,plain,
add(additive_identity,additive_identity) = additive_inverse(additive_identity),
inference(hyper_resolution,[status(thm)],[hi18,hi4,h27]) ).
cnf(t5316,plain,
additive_identity = additive_inverse(additive_identity),
inference(step,[status(thm)],[t11,t258]) ).
cnf(t431,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t5316]) ).
cnf(t5527,plain,
additive_inverse(X1) = add(X1,additive_identity),
inference(step,[status(thm)],[t5029,t431]) ).
cnf(t5528,plain,
additive_inverse(X1) = X1,
inference(step,[status(thm)],[t5527,t257]) ).
cnf(t5040,plain,
additive_inverse(X1) = X1,
inference(orient,[status(thm)],[t5528]) ).
cnf(t5531,plain,
multiply(c,add(b,a)) = additive_identity,
inference(step,[status(thm)],[t3897,t5040]) ).
cnf(t1614,plain,
multiply(c,b) = multiply(a,b),
inference(cp,[status(thm)],[t1613,t263]) ).
cnf(t5345,plain,
multiply(c,b) = c,
inference(step,[status(thm)],[t1614,t422]) ).
cnf(t1630,plain,
multiply(c,b) = c,
inference(orient,[status(thm)],[t5345]) ).
cnf(t1632,plain,
multiply(c,add(b,X1)) = add(c,multiply(c,X1)),
inference(cp,[status(thm)],[t394,t1630]) ).
cnf(t5374,plain,
multiply(c,add(b,X1)) = multiply(c,add(c,X1)),
inference(step,[status(thm)],[t1632,t1851]) ).
cnf(t2100,plain,
multiply(c,add(b,X1)) = multiply(c,add(c,X1)),
inference(orient,[status(thm)],[t5374]) ).
cnf(t5532,plain,
multiply(c,add(c,a)) = additive_identity,
inference(step,[status(thm)],[t5531,t2100]) ).
cnf(t5043,plain,
multiply(c,add(c,a)) = additive_identity,
inference(rw,[status(thm)],[t5532]) ).
cnf(t5204,plain,
multiply(c,add(c,a)) = additive_identity,
inference(orient,[status(thm)],[t5043]) ).
cnf(t5206,plain,
multiply(c,add(c,add(c,a))) = add(c,additive_identity),
inference(cp,[status(thm)],[t1851,t5204]) ).
cnf(t5020,plain,
add(X1,add(X1,X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t335,t4998]) ).
cnf(t5610,plain,
add(X1,add(X1,X2)) = X2,
inference(step,[status(thm)],[t5020,t258]) ).
cnf(t5165,plain,
add(X1,add(X1,X2)) = X2,
inference(orient,[status(thm)],[t5610]) ).
cnf(t5614,plain,
multiply(c,a) = add(c,additive_identity),
inference(step,[status(thm)],[t5206,t5165]) ).
cnf(t5615,plain,
multiply(c,a) = c,
inference(step,[status(thm)],[t5614,t257]) ).
cnf(t5216,plain,
multiply(c,a) = c,
inference(orient,[status(thm)],[t5615]) ).
cnf(t5617,plain,
multiply(b,c) = multiply(b,a),
inference(step,[status(thm)],[t1671,t5216]) ).
cnf(t1748,plain,
multiply(add(b,c),b) = add(b,c),
inference(cp,[status(thm)],[t1741,t1630]) ).
cnf(t5350,plain,
multiply(add(c,b),b) = add(b,c),
inference(step,[status(thm)],[t1748,t284]) ).
cnf(t5351,plain,
multiply(add(c,b),b) = add(c,b),
inference(step,[status(thm)],[t5350,t284]) ).
cnf(t1796,plain,
multiply(add(c,b),b) = add(c,b),
inference(orient,[status(thm)],[t5351]) ).
cnf(t3771,plain,
additive_identity = multiply(add(c,b),add(b,additive_inverse(add(c,b)))),
inference(cp,[status(thm)],[t3760,t1796]) ).
cnf(t5445,plain,
additive_identity = multiply(add(c,b),additive_inverse(c)),
inference(step,[status(thm)],[t3771,t2246]) ).
cnf(t3813,plain,
multiply(add(c,b),additive_inverse(c)) = additive_identity,
inference(orient,[status(thm)],[t5445]) ).
cnf(t3816,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t417,t3813]) ).
cnf(t5449,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = additive_identity,
inference(step,[status(thm)],[t3816,t430]) ).
cnf(t3930,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = additive_identity,
inference(orient,[status(thm)],[t5449]) ).
cnf(t3942,plain,
multiply(additive_inverse(c),add(c,b)) = multiply(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t432,t3930]) ).
cnf(t5450,plain,
multiply(additive_inverse(c),add(c,b)) = additive_identity,
inference(step,[status(thm)],[t3942,t428]) ).
cnf(t3943,plain,
multiply(additive_inverse(c),add(c,b)) = additive_identity,
inference(orient,[status(thm)],[t5450]) ).
cnf(t3945,plain,
multiply(add(add(c,b),additive_inverse(c)),add(c,b)) = add(add(c,b),additive_identity),
inference(cp,[status(thm)],[t1741,t3943]) ).
cnf(t5451,plain,
multiply(add(c,add(b,additive_inverse(c))),add(c,b)) = add(add(c,b),additive_identity),
inference(step,[status(thm)],[t3945,t335]) ).
cnf(t1681,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t1678,t284]) ).
cnf(t1724,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t1681]) ).
cnf(t5452,plain,
multiply(b,add(c,b)) = add(add(c,b),additive_identity),
inference(step,[status(thm)],[t5451,t1724]) ).
cnf(t5453,plain,
multiply(b,add(c,b)) = add(c,add(b,additive_identity)),
inference(step,[status(thm)],[t5452,t335]) ).
cnf(t5454,plain,
multiply(b,add(c,b)) = add(c,b),
inference(step,[status(thm)],[t5453,t257]) ).
cnf(t3953,plain,
multiply(b,add(c,b)) = add(c,b),
inference(orient,[status(thm)],[t5454]) ).
cnf(t3955,plain,
multiply(b,add(b,add(c,b))) = add(b,add(c,b)),
inference(cp,[status(thm)],[t1851,t3953]) ).
cnf(t5490,plain,
multiply(b,add(c,add(b,b))) = add(b,add(c,b)),
inference(step,[status(thm)],[t3955,t309]) ).
cnf(t5491,plain,
multiply(b,add(c,add(b,b))) = add(c,add(b,b)),
inference(step,[status(thm)],[t5490,t309]) ).
cnf(t4797,plain,
multiply(b,add(c,add(b,b))) = add(c,add(b,b)),
inference(orient,[status(thm)],[t5491]) ).
cnf(t5523,plain,
multiply(b,add(c,additive_identity)) = add(c,add(b,b)),
inference(step,[status(thm)],[t4797,t4998]) ).
cnf(t5524,plain,
multiply(b,c) = add(c,add(b,b)),
inference(step,[status(thm)],[t5523,t257]) ).
cnf(t5525,plain,
multiply(b,c) = add(c,additive_identity),
inference(step,[status(thm)],[t5524,t4998]) ).
cnf(t5526,plain,
multiply(b,c) = c,
inference(step,[status(thm)],[t5525,t257]) ).
cnf(t5039,plain,
multiply(b,c) = c,
inference(rw,[status(thm)],[t5526]) ).
cnf(t5106,plain,
multiply(b,c) = c,
inference(orient,[status(thm)],[t5039]) ).
cnf(t5618,plain,
c = multiply(b,a),
inference(step,[status(thm)],[t5617,t5106]) ).
cnf(t5230,plain,
c = multiply(b,a),
inference(rw,[status(thm)],[t5618]) ).
cnf(t5233,plain,
multiply(b,a) = c,
inference(orient,[status(thm)],[t5230]) ).
cnf(t5238,plain,
true = product(b,a,c),
inference(cp,[status(thm)],[t677,t5233]) ).
cnf(t5274,plain,
product(b,a,c) = true,
inference(orient,[status(thm)],[t5238]) ).
cnf(f21,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f21_nnf,plain,
~ product(b,a,c),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ product(b,a,c),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
product(b,a,c) != true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5274]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 07:45:54 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 30.41/4.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.41/4.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------