%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 42.14s 5.83s
% Output : Proof 42.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 21
% Syntax : Number of formulae : 248 ( 208 unt; 0 def)
% Number of atoms : 368 ( 172 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 : 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 : 527 ( 6 sgn 140 !; 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(t46,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t518,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/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(f23,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f23_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi23,axiom,
product(X0,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t159,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(hyper_resolution,[status(thm)],[hi16,hi23,h5]) ).
cnf(t464,plain,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(orient,[status(thm)],[t159]) ).
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(t234,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(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(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi3,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(t230,plain,
add(multiply(X1,X2),add(additive_identity,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h16,h21]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
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(t144,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,h17,h18]) ).
cnf(t299,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(orient,[status(thm)],[t144]) ).
cnf(t2501,plain,
add(additive_identity,add(multiply(X1,X3),multiply(X1,X2))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t230,t299]) ).
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(t2,plain,
add(additive_identity,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi15,hi0,hi3]) ).
cnf(t262,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t2502,plain,
add(multiply(X1,X3),multiply(X1,X2)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t2501,t262]) ).
cnf(t385,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X3,X2)),
inference(orient,[status(thm)],[t2502]) ).
cnf(t2505,plain,
multiply(X1,add(additive_identity,multiply(X2,X3))) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t234,t385]) ).
cnf(t2506,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t2505,t262]) ).
cnf(t412,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t2506]) ).
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(f24,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f24_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(hi24,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t95,plain,
add(multiply(additive_identity,b),multiply(a,b)) = c,
inference(hyper_resolution,[status(thm)],[hi16,hi24,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(t231,plain,
add(multiply(X1,X2),add(additive_identity,multiply(X3,X2))) = multiply(add(X1,X3),X2),
inference(hyper_resolution,[status(thm)],[hi15,h12,h21]) ).
cnf(t2498,plain,
add(additive_identity,add(multiply(X3,X2),multiply(X1,X2))) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t231,t299]) ).
cnf(t2499,plain,
add(multiply(X3,X2),multiply(X1,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t2498,t262]) ).
cnf(t373,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X3,X1),X2),
inference(orient,[status(thm)],[t2499]) ).
cnf(t2514,plain,
multiply(add(a,additive_identity),b) = c,
inference(step,[status(thm)],[t95,t373]) ).
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(t2515,plain,
multiply(a,b) = c,
inference(step,[status(thm)],[t2514,t257]) ).
cnf(t443,plain,
multiply(a,b) = c,
inference(orient,[status(thm)],[t2515]) ).
cnf(t445,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(cp,[status(thm)],[t412,t443]) ).
cnf(t1687,plain,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(orient,[status(thm)],[t445]) ).
cnf(t1704,plain,
multiply(b,a) = multiply(b,multiply(c,a)),
inference(cp,[status(thm)],[t464,t1687]) ).
cnf(t1757,plain,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(orient,[status(thm)],[t1704]) ).
cnf(t5,plain,
multiply(X1,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi2,hi23]) ).
cnf(t264,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t376,plain,
multiply(add(X1,X2),X2) = add(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t373,t264]) ).
cnf(t2022,plain,
add(X1,multiply(X2,X1)) = multiply(add(X2,X1),X1),
inference(orient,[status(thm)],[t376]) ).
cnf(t388,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t385,t264]) ).
cnf(t2332,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,X1)),
inference(orient,[status(thm)],[t388]) ).
cnf(t414,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t412,t264]) ).
cnf(t1639,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t414]) ).
cnf(t467,plain,
multiply(a,b) = multiply(a,multiply(b,c)),
inference(cp,[status(thm)],[t464,t443]) ).
cnf(t2546,plain,
c = multiply(a,multiply(b,c)),
inference(step,[status(thm)],[t467,t443]) ).
cnf(t1601,plain,
multiply(a,multiply(b,c)) = c,
inference(orient,[status(thm)],[t2546]) ).
cnf(t1641,plain,
multiply(a,multiply(b,c)) = multiply(a,c),
inference(cp,[status(thm)],[t1639,t1601]) ).
cnf(t2547,plain,
c = multiply(a,c),
inference(step,[status(thm)],[t1641,t1601]) ).
cnf(t1661,plain,
multiply(a,c) = c,
inference(orient,[status(thm)],[t2547]) ).
cnf(t2036,plain,
multiply(add(a,c),c) = add(c,c),
inference(cp,[status(thm)],[t2022,t1661]) ).
cnf(t20,plain,
add(X1,X2) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h17]) ).
cnf(t274,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t20]) ).
cnf(t2571,plain,
multiply(add(c,a),c) = add(c,c),
inference(step,[status(thm)],[t2036,t274]) ).
cnf(h15,plain,
product(V0,V1,add(multiply(V0,additive_identity),multiply(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi2,hi2,hi0,hi3]) ).
cnf(f22,axiom,
product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_inverse) ).
fof(f22_nnf,plain,
! [X,Y] : product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y] : product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
product(X0,additive_inverse(X1),additive_inverse(multiply(X0,X1))),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi22,axiom,
product(X0,additive_inverse(X1),additive_inverse(multiply(X0,X1))) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t221,plain,
add(multiply(X1,additive_identity),multiply(X1,additive_inverse(X2))) = additive_inverse(multiply(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi16,hi22,h15]) ).
cnf(t2509,plain,
multiply(X1,add(additive_inverse(X2),additive_identity)) = additive_inverse(multiply(X1,X2)),
inference(step,[status(thm)],[t221,t385]) ).
cnf(t2510,plain,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inference(step,[status(thm)],[t2509,t257]) ).
cnf(t428,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(orient,[status(thm)],[t2510]) ).
cnf(t429,plain,
multiply(X1,additive_inverse(X1)) = additive_inverse(X1),
inference(cp,[status(thm)],[t428,t264]) ).
cnf(t1555,plain,
multiply(X1,additive_inverse(X1)) = additive_inverse(X1),
inference(orient,[status(thm)],[t429]) ).
cnf(t2026,plain,
multiply(add(X1,additive_inverse(X1)),additive_inverse(X1)) = add(additive_inverse(X1),additive_inverse(X1)),
inference(cp,[status(thm)],[t2022,t1555]) ).
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(t2497,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t37,t262]) ).
cnf(t362,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t2497]) ).
cnf(t2554,plain,
multiply(additive_identity,additive_inverse(X1)) = add(additive_inverse(X1),additive_inverse(X1)),
inference(step,[status(thm)],[t2026,t362]) ).
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(f20,axiom,
product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_additive_id2) ).
fof(f20_nnf,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] : product(additive_identity,X,additive_identity),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
product(additive_identity,X0,additive_identity) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t90,plain,
add(multiply(additive_identity,X1),multiply(additive_identity,X1)) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi16,hi20,h10]) ).
cnf(t2512,plain,
multiply(add(additive_identity,additive_identity),X1) = additive_identity,
inference(step,[status(thm)],[t90,t373]) ).
cnf(t2513,plain,
multiply(additive_identity,X1) = additive_identity,
inference(step,[status(thm)],[t2512,t262]) ).
cnf(t441,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t2513]) ).
cnf(t2555,plain,
additive_identity = add(additive_inverse(X1),additive_inverse(X1)),
inference(step,[status(thm)],[t2554,t441]) ).
cnf(h23,plain,
sum(V0,V1,add(additive_identity,add(V0,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,hi3,hi3]) ).
cnf(f21,axiom,
sum(additive_inverse(X),additive_inverse(Y),additive_inverse(add(X,Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute_additive_inverse) ).
fof(f21_nnf,plain,
! [X,Y] : sum(additive_inverse(X),additive_inverse(Y),additive_inverse(add(X,Y))),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y] : sum(additive_inverse(X),additive_inverse(Y),additive_inverse(add(X,Y))),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X0,X1))),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X0,X1))) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t164,plain,
add(additive_identity,add(additive_inverse(X1),additive_inverse(X2))) = additive_inverse(add(X1,X2)),
inference(hyper_resolution,[status(thm)],[hi15,hi21,h23]) ).
cnf(t2516,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(step,[status(thm)],[t164,t262]) ).
cnf(t450,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X1,X2)),
inference(orient,[status(thm)],[t2516]) ).
cnf(t2556,plain,
additive_identity = additive_inverse(add(X1,X1)),
inference(step,[status(thm)],[t2555,t450]) ).
cnf(t2061,plain,
additive_inverse(add(X1,X1)) = additive_identity,
inference(orient,[status(thm)],[t2556]) ).
cnf(t145,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,hi3,h18]) ).
cnf(t325,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t145]) ).
cnf(t365,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t325,t362]) ).
cnf(t2553,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t365,t262]) ).
cnf(t1765,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t2553]) ).
cnf(t1769,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t1765,t274]) ).
cnf(t1906,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t1769]) ).
cnf(t1909,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X1,X2))),
inference(cp,[status(thm)],[t1906,t450]) ).
cnf(t1997,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(orient,[status(thm)],[t1909]) ).
cnf(t2077,plain,
additive_inverse(X1) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1997,t2061]) ).
cnf(t2557,plain,
additive_inverse(X1) = X1,
inference(step,[status(thm)],[t2077,t257]) ).
cnf(t2086,plain,
additive_inverse(X1) = X1,
inference(orient,[status(thm)],[t2557]) ).
cnf(t2558,plain,
add(X1,X1) = additive_identity,
inference(step,[status(thm)],[t2061,t2086]) ).
cnf(t2087,plain,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[t2558]) ).
cnf(t2095,plain,
add(X1,X1) = additive_identity,
inference(orient,[status(thm)],[t2087]) ).
cnf(t2572,plain,
multiply(add(c,a),c) = additive_identity,
inference(step,[status(thm)],[t2571,t2095]) ).
cnf(t2180,plain,
multiply(add(c,a),c) = additive_identity,
inference(orient,[status(thm)],[t2572]) ).
cnf(t2339,plain,
multiply(add(c,a),add(c,add(c,a))) = add(add(c,a),additive_identity),
inference(cp,[status(thm)],[t2332,t2180]) ).
cnf(t1767,plain,
additive_inverse(X1) = add(X2,additive_inverse(add(X2,X1))),
inference(cp,[status(thm)],[t1765,t450]) ).
cnf(t1971,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(orient,[status(thm)],[t1767]) ).
cnf(t2564,plain,
add(X1,add(X1,X2)) = additive_inverse(X2),
inference(step,[status(thm)],[t1971,t2086]) ).
cnf(t2565,plain,
add(X1,add(X1,X2)) = X2,
inference(step,[status(thm)],[t2564,t2086]) ).
cnf(t2092,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[t2565]) ).
cnf(t2150,plain,
add(X1,add(X1,X2)) = X2,
inference(orient,[status(thm)],[t2092]) ).
cnf(t2584,plain,
multiply(add(c,a),a) = add(add(c,a),additive_identity),
inference(step,[status(thm)],[t2339,t2150]) ).
cnf(t2585,plain,
multiply(add(c,a),a) = add(c,add(a,additive_identity)),
inference(step,[status(thm)],[t2584,t325]) ).
cnf(t2586,plain,
multiply(add(c,a),a) = add(c,a),
inference(step,[status(thm)],[t2585,t257]) ).
cnf(t2416,plain,
multiply(add(c,a),a) = add(c,a),
inference(orient,[status(thm)],[t2586]) ).
cnf(t2417,plain,
multiply(add(add(c,a),a),a) = add(a,add(c,a)),
inference(cp,[status(thm)],[t2022,t2416]) ).
cnf(t2587,plain,
multiply(add(c,add(a,a)),a) = add(a,add(c,a)),
inference(step,[status(thm)],[t2417,t325]) ).
cnf(t2588,plain,
multiply(add(c,additive_identity),a) = add(a,add(c,a)),
inference(step,[status(thm)],[t2587,t2095]) ).
cnf(t2589,plain,
multiply(c,a) = add(a,add(c,a)),
inference(step,[status(thm)],[t2588,t257]) ).
cnf(t2562,plain,
add(X1,add(X2,X1)) = additive_inverse(X2),
inference(step,[status(thm)],[t1997,t2086]) ).
cnf(t2563,plain,
add(X1,add(X2,X1)) = X2,
inference(step,[status(thm)],[t2562,t2086]) ).
cnf(t2091,plain,
add(X1,add(X2,X1)) = X2,
inference(rw,[status(thm)],[t2563]) ).
cnf(t2132,plain,
add(X1,add(X2,X1)) = X2,
inference(orient,[status(thm)],[t2091]) ).
cnf(t2590,plain,
multiply(c,a) = c,
inference(step,[status(thm)],[t2589,t2132]) ).
cnf(t2426,plain,
multiply(c,a) = c,
inference(orient,[status(thm)],[t2590]) ).
cnf(t2591,plain,
multiply(b,c) = multiply(b,a),
inference(step,[status(thm)],[t1757,t2426]) ).
cnf(t1688,plain,
multiply(c,b) = multiply(a,b),
inference(cp,[status(thm)],[t1687,t264]) ).
cnf(t2549,plain,
multiply(c,b) = c,
inference(step,[status(thm)],[t1688,t443]) ).
cnf(t1705,plain,
multiply(c,b) = c,
inference(orient,[status(thm)],[t2549]) ).
cnf(t2031,plain,
multiply(add(c,b),b) = add(b,c),
inference(cp,[status(thm)],[t2022,t1705]) ).
cnf(t2570,plain,
multiply(add(c,b),b) = add(c,b),
inference(step,[status(thm)],[t2031,t274]) ).
cnf(t2166,plain,
multiply(add(c,b),b) = add(c,b),
inference(orient,[status(thm)],[t2570]) ).
cnf(t2338,plain,
multiply(add(c,b),add(b,add(c,b))) = add(add(c,b),add(c,b)),
inference(cp,[status(thm)],[t2332,t2166]) ).
cnf(t2575,plain,
multiply(add(c,b),c) = add(add(c,b),add(c,b)),
inference(step,[status(thm)],[t2338,t2132]) ).
cnf(t2576,plain,
multiply(add(c,b),c) = add(c,add(b,add(c,b))),
inference(step,[status(thm)],[t2575,t325]) ).
cnf(t2577,plain,
multiply(add(c,b),c) = add(c,c),
inference(step,[status(thm)],[t2576,t2132]) ).
cnf(t2578,plain,
multiply(add(c,b),c) = additive_identity,
inference(step,[status(thm)],[t2577,t2095]) ).
cnf(t2365,plain,
multiply(add(c,b),c) = additive_identity,
inference(orient,[status(thm)],[t2578]) ).
cnf(t2366,plain,
multiply(add(add(c,b),c),c) = add(c,additive_identity),
inference(cp,[status(thm)],[t2022,t2365]) ).
cnf(t2579,plain,
multiply(add(c,add(b,c)),c) = add(c,additive_identity),
inference(step,[status(thm)],[t2366,t325]) ).
cnf(t2580,plain,
multiply(b,c) = add(c,additive_identity),
inference(step,[status(thm)],[t2579,t2132]) ).
cnf(t2581,plain,
multiply(b,c) = c,
inference(step,[status(thm)],[t2580,t257]) ).
cnf(t2374,plain,
multiply(b,c) = c,
inference(orient,[status(thm)],[t2581]) ).
cnf(t2592,plain,
c = multiply(b,a),
inference(step,[status(thm)],[t2591,t2374]) ).
cnf(t2436,plain,
c = multiply(b,a),
inference(rw,[status(thm)],[t2592]) ).
cnf(t2437,plain,
multiply(b,a) = c,
inference(orient,[status(thm)],[t2436]) ).
cnf(t2440,plain,
true = product(b,a,c),
inference(cp,[status(thm)],[t518,t2437]) ).
cnf(t2469,plain,
product(b,a,c) = true,
inference(orient,[status(thm)],[t2440]) ).
cnf(f25,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
fof(f25_nnf,plain,
~ product(b,a,c),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ product(b,a,c),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(goal_0,negated_conjecture,
product(b,a,c) != true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2469]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:43:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.14/5.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.14/5.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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