%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 17.35s 4.90s
% Output : Proof 17.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 22
% Syntax : Number of formulae : 305 ( 261 unt; 0 def)
% Number of atoms : 437 ( 225 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 270 ( 138 ~; 132 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 615 ( 21 sgn 148 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f2_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t49,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t428,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(f10,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
fof(f10_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X0,X4,X5),true,product(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h5,plain,
product(multiply(V0,V1),V2,multiply(V0,multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi2,hi2,hi2]) ).
cnf(f16,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f16_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f19,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox/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(t146,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(hyper_resolution,[status(thm)],[hi16,hi19,h5]) ).
cnf(t379,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(orient,[status(thm)],[t146]) ).
cnf(f12,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f12_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f1,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f1_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
sum(X0,additive_identity,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f3,axiom,
sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f3_nnf,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : sum(X,Y,add(X,Y)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h14,plain,
product(V0,V1,add(multiply(V0,V1),multiply(V0,additive_identity))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2,hi2,hi1,hi3]) ).
cnf(f9,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
fof(f9_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X2,X3,X5),true,product(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h6,plain,
product(V0,multiply(V1,V2),multiply(multiply(V0,V1),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi2,hi2,hi2]) ).
cnf(t238,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/sandbox/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/sandbox/benchmark/theBenchmark.p',distributivity1) ).
fof(f11_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(product(X0,X5,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h16,plain,
sum(multiply(V0,V1),multiply(V0,V2),multiply(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi2,hi2,hi3,hi2]) ).
cnf(f15,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f15_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t231,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/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f7_nnf,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X0,X4,X5),true,sum(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(t144,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t288,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t144]) ).
cnf(t5400,plain,
add(multiply(X1,X2),add(multiply(X1,X3),additive_identity)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t231,t288]) ).
cnf(f8,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h17,plain,
sum(V0,V1,add(V1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3]) ).
cnf(t143,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,h17,h18]) ).
cnf(t274,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(orient,[status(thm)],[t143]) ).
cnf(t5401,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t5400,t274]) ).
cnf(f0,axiom,
sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
fof(f0_nnf,plain,
! [X] : sum(additive_identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : sum(additive_identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
sum(additive_identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h28,plain,
sum(add(additive_identity,V0),additive_identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi1,hi0]) ).
cnf(h22,plain,
sum(V0,additive_identity,add(V0,additive_identity)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi1,hi3]) ).
cnf(t23,plain,
add(add(additive_identity,X1),additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi15,h22,h28]) ).
cnf(t1,plain,
add(X1,additive_identity) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi1,hi3]) ).
cnf(t257,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t5391,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t23,t257]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t5391]) ).
cnf(t5402,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t5401,t258]) ).
cnf(t327,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t5402]) ).
cnf(t5404,plain,
multiply(X1,add(multiply(X2,X3),additive_identity)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t238,t327]) ).
cnf(t5405,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t5404,t257]) ).
cnf(t350,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t5405]) ).
cnf(f14,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
fof(f14_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X5,X1,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h11,plain,
product(V0,V1,add(multiply(additive_identity,V1),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi0,hi3]) ).
cnf(f20,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/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(t96,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/sandbox/benchmark/theBenchmark.p',distributivity3) ).
fof(f13_nnf,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(sum(X0,X3,X5),true,ifeq(product(X5,X1,X6),true,sum(X2,X4,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h12,plain,
sum(multiply(V0,V1),multiply(V2,V1),multiply(add(V0,V2),V1)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi2,hi2,hi3,hi2]) ).
cnf(t232,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(t5397,plain,
add(multiply(X1,X2),add(multiply(X3,X2),additive_identity)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t232,t288]) ).
cnf(t5398,plain,
add(additive_identity,add(multiply(X1,X2),multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t5397,t274]) ).
cnf(t5399,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t5398,t258]) ).
cnf(t319,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t5399]) ).
cnf(t5410,plain,
multiply(add(additive_identity,a),b) = c,
inference(step,[status(thm)],[t96,t319]) ).
cnf(t5411,plain,
multiply(a,b) = c,
inference(step,[status(thm)],[t5410,t258]) ).
cnf(t372,plain,
multiply(a,b) = c,
inference(orient,[status(thm)],[t5411]) ).
cnf(t373,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(cp,[status(thm)],[t350,t372]) ).
cnf(t1474,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(orient,[status(thm)],[t373]) ).
cnf(t1490,plain,
multiply(b,a) = multiply(b,multiply(c,a)),
inference(cp,[status(thm)],[t379,t1474]) ).
cnf(t1532,plain,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(orient,[status(thm)],[t1490]) ).
cnf(t6,plain,
multiply(X1,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi2,hi19]) ).
cnf(t263,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t330,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t327,t263]) ).
cnf(t1712,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(orient,[status(thm)],[t330]) ).
cnf(t352,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t350,t263]) ).
cnf(t1441,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t352]) ).
cnf(t1451,plain,
multiply(X1,add(multiply(X1,X2),X3)) = add(multiply(X1,X2),multiply(X1,X3)),
inference(cp,[status(thm)],[t327,t1441]) ).
cnf(t5532,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t1451,t327]) ).
cnf(t3514,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t5532]) ).
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/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_inverse(X),additive_identity),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
sum(X0,additive_inverse(X0),additive_identity) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t37,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(t5396,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t37,t258]) ).
cnf(t313,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5396]) ).
cnf(t3521,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = multiply(X1,additive_identity),
inference(cp,[status(thm)],[t3514,t313]) ).
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(t99,plain,
multiply(add(X1,X1),additive_identity) = multiply(X1,additive_identity),
inference(hyper_resolution,[status(thm)],[hi15,h4,h12]) ).
cnf(h9,plain,
product(add(V0,V1),V2,add(multiply(V0,V2),multiply(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi3,hi3]) ).
cnf(f17,axiom,
product(X,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_times_identity_x_is_identity) ).
fof(f17_nnf,plain,
! [X] : product(X,additive_identity,additive_identity),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] : product(X,additive_identity,additive_identity),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
product(X0,additive_identity,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t85,plain,
add(multiply(X1,additive_identity),multiply(X2,additive_identity)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi16,hi17,h9]) ).
cnf(t5406,plain,
multiply(add(X1,X2),additive_identity) = additive_identity,
inference(step,[status(thm)],[t85,t319]) ).
cnf(t355,plain,
multiply(add(X1,X2),additive_identity) = additive_identity,
inference(orient,[status(thm)],[t5406]) ).
cnf(t5413,plain,
additive_identity = multiply(X1,additive_identity),
inference(step,[status(thm)],[t99,t355]) ).
cnf(t427,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t5413]) ).
cnf(t5533,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(step,[status(thm)],[t3521,t427]) ).
cnf(t3592,plain,
multiply(X1,add(X2,additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t5533]) ).
cnf(t321,plain,
multiply(add(X1,X2),X1) = add(X1,multiply(X2,X1)),
inference(cp,[status(thm)],[t319,t263]) ).
cnf(t1602,plain,
add(X1,multiply(X2,X1)) = multiply(add(X1,X2),X1),
inference(orient,[status(thm)],[t321]) ).
cnf(t1614,plain,
multiply(add(b,a),b) = add(b,c),
inference(cp,[status(thm)],[t1602,t372]) ).
cnf(t20,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h17]) ).
cnf(t273,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t20]) ).
cnf(t5444,plain,
multiply(add(b,a),b) = add(c,b),
inference(step,[status(thm)],[t1614,t273]) ).
cnf(t1683,plain,
multiply(add(b,a),b) = add(c,b),
inference(orient,[status(thm)],[t5444]) ).
cnf(t3602,plain,
additive_identity = multiply(add(b,a),add(b,additive_inverse(add(c,b)))),
inference(cp,[status(thm)],[t3592,t1683]) ).
cnf(t315,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t288,t313]) ).
cnf(t5439,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t315,t258]) ).
cnf(t1539,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t5439]) ).
cnf(t103,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h18]) ).
cnf(t297,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(orient,[status(thm)],[t103]) ).
cnf(t1542,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = add(X2,additive_identity),
inference(cp,[status(thm)],[t1539,t297]) ).
cnf(t5478,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(step,[status(thm)],[t1542,t257]) ).
cnf(t2085,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(orient,[status(thm)],[t5478]) ).
cnf(t1541,plain,
additive_inverse(additive_inverse(X1)) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1539,t313]) ).
cnf(t5440,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t1541,t257]) ).
cnf(t1556,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t5440]) ).
cnf(t2092,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t2085,t1556]) ).
cnf(t2107,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t2092]) ).
cnf(t5534,plain,
additive_identity = multiply(add(b,a),additive_inverse(c)),
inference(step,[status(thm)],[t3602,t2107]) ).
cnf(t3635,plain,
multiply(add(b,a),additive_inverse(c)) = additive_identity,
inference(orient,[status(thm)],[t5534]) ).
cnf(t3639,plain,
multiply(add(b,a),multiply(additive_inverse(c),X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t350,t3635]) ).
cnf(h10,plain,
product(V0,V1,add(multiply(V0,V1),multiply(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi2,hi2,hi1,hi3]) ).
cnf(f18,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_times_x_is_identity) ).
fof(f18_nnf,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
product(additive_identity,X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t91,plain,
add(multiply(additive_identity,X1),multiply(additive_identity,X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi16,hi18,h10]) ).
cnf(t5408,plain,
multiply(add(additive_identity,additive_identity),X1) = additive_identity,
inference(step,[status(thm)],[t91,t319]) ).
cnf(t5409,plain,
multiply(additive_identity,X1) = additive_identity,
inference(step,[status(thm)],[t5408,t258]) ).
cnf(t371,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t5409]) ).
cnf(t5537,plain,
multiply(add(b,a),multiply(additive_inverse(c),X1)) = additive_identity,
inference(step,[status(thm)],[t3639,t371]) ).
cnf(t3716,plain,
multiply(add(b,a),multiply(additive_inverse(c),X1)) = additive_identity,
inference(orient,[status(thm)],[t5537]) ).
cnf(t3728,plain,
multiply(additive_inverse(c),add(b,a)) = multiply(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t379,t3716]) ).
cnf(t5538,plain,
multiply(additive_inverse(c),add(b,a)) = additive_identity,
inference(step,[status(thm)],[t3728,t427]) ).
cnf(t3729,plain,
multiply(additive_inverse(c),add(b,a)) = additive_identity,
inference(orient,[status(thm)],[t5538]) ).
cnf(t2116,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X2,X1))),
inference(cp,[status(thm)],[t2107,t273]) ).
cnf(t2175,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(orient,[status(thm)],[t2116]) ).
cnf(t1452,plain,
multiply(X1,add(X2,multiply(X1,X3))) = add(multiply(X1,X2),multiply(X1,X3)),
inference(cp,[status(thm)],[t327,t1441]) ).
cnf(t5548,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t1452,t327]) ).
cnf(t3895,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t5548]) ).
cnf(t3898,plain,
multiply(X1,add(X2,X2)) = multiply(X1,multiply(add(X2,X1),X2)),
inference(cp,[status(thm)],[t3895,t1602]) ).
cnf(t4924,plain,
multiply(X1,multiply(add(X2,X1),X2)) = multiply(X1,add(X2,X2)),
inference(orient,[status(thm)],[t3898]) ).
cnf(t4936,plain,
multiply(additive_inverse(X1),add(X1,X1)) = multiply(additive_inverse(X1),multiply(additive_identity,X1)),
inference(cp,[status(thm)],[t4924,t313]) ).
cnf(t5586,plain,
multiply(additive_inverse(X1),add(X1,X1)) = multiply(additive_inverse(X1),additive_identity),
inference(step,[status(thm)],[t4936,t371]) ).
cnf(t5587,plain,
multiply(additive_inverse(X1),add(X1,X1)) = additive_identity,
inference(step,[status(thm)],[t5586,t427]) ).
cnf(t5009,plain,
multiply(additive_inverse(X1),add(X1,X1)) = additive_identity,
inference(orient,[status(thm)],[t5587]) ).
cnf(t5012,plain,
additive_identity = multiply(X1,add(additive_inverse(X1),additive_inverse(X1))),
inference(cp,[status(thm)],[t5009,t1556]) ).
cnf(t2127,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(cp,[status(thm)],[t1539,t2107]) ).
cnf(t2130,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(orient,[status(thm)],[t2127]) ).
cnf(t2133,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(cp,[status(thm)],[t2130,t1556]) ).
cnf(t2157,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(orient,[status(thm)],[t2133]) ).
cnf(t5588,plain,
additive_identity = multiply(X1,additive_inverse(add(X1,X1))),
inference(step,[status(thm)],[t5012,t2157]) ).
cnf(t5031,plain,
multiply(X1,additive_inverse(add(X1,X1))) = additive_identity,
inference(orient,[status(thm)],[t5588]) ).
cnf(t5045,plain,
multiply(X1,add(X1,additive_inverse(add(X1,X1)))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1712,t5031]) ).
cnf(t5589,plain,
multiply(X1,additive_inverse(X1)) = add(X1,additive_identity),
inference(step,[status(thm)],[t5045,t2107]) ).
cnf(t5590,plain,
multiply(X1,additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t5589,t257]) ).
cnf(t5067,plain,
multiply(X1,additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t5590]) ).
cnf(t5078,plain,
multiply(X1,add(X1,additive_inverse(X1))) = add(X1,X1),
inference(cp,[status(thm)],[t1712,t5067]) ).
cnf(t5591,plain,
multiply(X1,additive_identity) = add(X1,X1),
inference(step,[status(thm)],[t5078,t313]) ).
cnf(t5592,plain,
additive_identity = add(X1,X1),
inference(step,[status(thm)],[t5591,t427]) ).
cnf(t5102,plain,
add(X1,X1) = additive_identity,
inference(orient,[status(thm)],[t5592]) ).
cnf(t5133,plain,
additive_inverse(X1) = add(X1,additive_inverse(additive_identity)),
inference(cp,[status(thm)],[t2175,t5102]) ).
cnf(h24,plain,
sum(V0,additive_identity,add(additive_identity,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,hi1,hi3]) ).
cnf(f4,axiom,
sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/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(t10,plain,
add(additive_identity,additive_inverse(additive_identity)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi4,h24]) ).
cnf(t5412,plain,
additive_inverse(additive_identity) = additive_identity,
inference(step,[status(thm)],[t10,t258]) ).
cnf(t378,plain,
additive_inverse(additive_identity) = additive_identity,
inference(orient,[status(thm)],[t5412]) ).
cnf(t5619,plain,
additive_inverse(X1) = add(X1,additive_identity),
inference(step,[status(thm)],[t5133,t378]) ).
cnf(t5620,plain,
additive_inverse(X1) = X1,
inference(step,[status(thm)],[t5619,t257]) ).
cnf(t5145,plain,
additive_inverse(X1) = X1,
inference(orient,[status(thm)],[t5620]) ).
cnf(t5623,plain,
multiply(c,add(b,a)) = additive_identity,
inference(step,[status(thm)],[t3729,t5145]) ).
cnf(t1475,plain,
multiply(c,b) = multiply(a,b),
inference(cp,[status(thm)],[t1474,t263]) ).
cnf(t5436,plain,
multiply(c,b) = c,
inference(step,[status(thm)],[t1475,t372]) ).
cnf(t1491,plain,
multiply(c,b) = c,
inference(orient,[status(thm)],[t5436]) ).
cnf(t1493,plain,
multiply(c,add(b,X1)) = add(c,multiply(c,X1)),
inference(cp,[status(thm)],[t327,t1491]) ).
cnf(t5466,plain,
multiply(c,add(b,X1)) = multiply(c,add(c,X1)),
inference(step,[status(thm)],[t1493,t1712]) ).
cnf(t1961,plain,
multiply(c,add(b,X1)) = multiply(c,add(c,X1)),
inference(orient,[status(thm)],[t5466]) ).
cnf(t5624,plain,
multiply(c,add(c,a)) = additive_identity,
inference(step,[status(thm)],[t5623,t1961]) ).
cnf(t5148,plain,
multiply(c,add(c,a)) = additive_identity,
inference(rw,[status(thm)],[t5624]) ).
cnf(t5291,plain,
multiply(c,add(c,a)) = additive_identity,
inference(orient,[status(thm)],[t5148]) ).
cnf(t5293,plain,
multiply(c,add(c,add(c,a))) = add(c,additive_identity),
inference(cp,[status(thm)],[t1712,t5291]) ).
cnf(t5118,plain,
add(X1,add(X1,X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t288,t5102]) ).
cnf(t5702,plain,
add(X1,add(X1,X2)) = X2,
inference(step,[status(thm)],[t5118,t258]) ).
cnf(t5268,plain,
add(X1,add(X1,X2)) = X2,
inference(orient,[status(thm)],[t5702]) ).
cnf(t5705,plain,
multiply(c,a) = add(c,additive_identity),
inference(step,[status(thm)],[t5293,t5268]) ).
cnf(t5706,plain,
multiply(c,a) = c,
inference(step,[status(thm)],[t5705,t257]) ).
cnf(t5306,plain,
multiply(c,a) = c,
inference(orient,[status(thm)],[t5706]) ).
cnf(t5708,plain,
multiply(b,c) = multiply(b,a),
inference(step,[status(thm)],[t1532,t5306]) ).
cnf(t1609,plain,
multiply(add(b,c),b) = add(b,c),
inference(cp,[status(thm)],[t1602,t1491]) ).
cnf(t5442,plain,
multiply(add(c,b),b) = add(b,c),
inference(step,[status(thm)],[t1609,t273]) ).
cnf(t5443,plain,
multiply(add(c,b),b) = add(c,b),
inference(step,[status(thm)],[t5442,t273]) ).
cnf(t1657,plain,
multiply(add(c,b),b) = add(c,b),
inference(orient,[status(thm)],[t5443]) ).
cnf(t3603,plain,
additive_identity = multiply(add(c,b),add(b,additive_inverse(add(c,b)))),
inference(cp,[status(thm)],[t3592,t1657]) ).
cnf(t5535,plain,
additive_identity = multiply(add(c,b),additive_inverse(c)),
inference(step,[status(thm)],[t3603,t2107]) ).
cnf(t3645,plain,
multiply(add(c,b),additive_inverse(c)) = additive_identity,
inference(orient,[status(thm)],[t5535]) ).
cnf(t3648,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t350,t3645]) ).
cnf(t5539,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = additive_identity,
inference(step,[status(thm)],[t3648,t371]) ).
cnf(t3762,plain,
multiply(add(c,b),multiply(additive_inverse(c),X1)) = additive_identity,
inference(orient,[status(thm)],[t5539]) ).
cnf(t3774,plain,
multiply(additive_inverse(c),add(c,b)) = multiply(additive_inverse(c),additive_identity),
inference(cp,[status(thm)],[t379,t3762]) ).
cnf(t5540,plain,
multiply(additive_inverse(c),add(c,b)) = additive_identity,
inference(step,[status(thm)],[t3774,t427]) ).
cnf(t3775,plain,
multiply(additive_inverse(c),add(c,b)) = additive_identity,
inference(orient,[status(thm)],[t5540]) ).
cnf(t3777,plain,
multiply(add(add(c,b),additive_inverse(c)),add(c,b)) = add(add(c,b),additive_identity),
inference(cp,[status(thm)],[t1602,t3775]) ).
cnf(t5541,plain,
multiply(add(c,add(b,additive_inverse(c))),add(c,b)) = add(add(c,b),additive_identity),
inference(step,[status(thm)],[t3777,t288]) ).
cnf(t1543,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t1539,t273]) ).
cnf(t1585,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t1543]) ).
cnf(t5542,plain,
multiply(b,add(c,b)) = add(add(c,b),additive_identity),
inference(step,[status(thm)],[t5541,t1585]) ).
cnf(t5543,plain,
multiply(b,add(c,b)) = add(c,add(b,additive_identity)),
inference(step,[status(thm)],[t5542,t288]) ).
cnf(t5544,plain,
multiply(b,add(c,b)) = add(c,b),
inference(step,[status(thm)],[t5543,t257]) ).
cnf(t3785,plain,
multiply(b,add(c,b)) = add(c,b),
inference(orient,[status(thm)],[t5544]) ).
cnf(t3787,plain,
multiply(b,add(b,add(c,b))) = add(b,add(c,b)),
inference(cp,[status(thm)],[t1712,t3785]) ).
cnf(t278,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(cp,[status(thm)],[t274,t273]) ).
cnf(t3418,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(orient,[status(thm)],[t278]) ).
cnf(t5582,plain,
multiply(b,add(c,add(b,b))) = add(b,add(c,b)),
inference(step,[status(thm)],[t3787,t3418]) ).
cnf(t5583,plain,
multiply(b,add(c,add(b,b))) = add(c,add(b,b)),
inference(step,[status(thm)],[t5582,t3418]) ).
cnf(t4881,plain,
multiply(b,add(c,add(b,b))) = add(c,add(b,b)),
inference(orient,[status(thm)],[t5583]) ).
cnf(t5615,plain,
multiply(b,add(c,additive_identity)) = add(c,add(b,b)),
inference(step,[status(thm)],[t4881,t5102]) ).
cnf(t5616,plain,
multiply(b,c) = add(c,add(b,b)),
inference(step,[status(thm)],[t5615,t257]) ).
cnf(t5617,plain,
multiply(b,c) = add(c,additive_identity),
inference(step,[status(thm)],[t5616,t5102]) ).
cnf(t5618,plain,
multiply(b,c) = c,
inference(step,[status(thm)],[t5617,t257]) ).
cnf(t5144,plain,
multiply(b,c) = c,
inference(rw,[status(thm)],[t5618]) ).
cnf(t5211,plain,
multiply(b,c) = c,
inference(orient,[status(thm)],[t5144]) ).
cnf(t5709,plain,
c = multiply(b,a),
inference(step,[status(thm)],[t5708,t5211]) ).
cnf(t5322,plain,
c = multiply(b,a),
inference(rw,[status(thm)],[t5709]) ).
cnf(t5325,plain,
multiply(b,a) = c,
inference(orient,[status(thm)],[t5322]) ).
cnf(t5330,plain,
true = product(b,a,c),
inference(cp,[status(thm)],[t428,t5325]) ).
cnf(t5368,plain,
product(b,a,c) = true,
inference(orient,[status(thm)],[t5330]) ).
cnf(f21,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/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,t5368]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 07:41:37 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.35/4.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.35/4.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------