%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 02:37:24 PM UTC 2026
% Result : Unsatisfiable 33.00s 9.73s
% Output : Proof 33.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 189 ( 149 unt; 0 def)
% Number of atoms : 309 ( 128 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 246 ( 126 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 498 ( 8 sgn 130 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t40,plain,
sum(X1,X2,add(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t366,plain,
sum(X1,X2,add(X1,X2)) = true,
inference(orient,[status(thm)],[t40]) ).
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(hi3,axiom,
sum(X0,X1,add(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
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(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(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(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
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(t229,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(h21,plain,
sum(V0,V1,add(V0,add(additive_identity,V1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,hi3,hi3]) ).
cnf(h18,plain,
sum(add(V0,V1),V2,add(V0,add(V1,V2))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi3,hi3]) ).
cnf(t188,plain,
add(add(X1,X2),add(additive_identity,X3)) = add(X1,add(X2,X3)),
inference(hyper_resolution,[status(thm)],[hi15,h18,h21]) ).
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(t18,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(t2144,plain,
add(additive_identity,X1) = X1,
inference(step,[status(thm)],[t18,t257]) ).
cnf(t258,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t2144]) ).
cnf(t2150,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(step,[status(thm)],[t188,t258]) ).
cnf(t274,plain,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
inference(orient,[status(thm)],[t2150]) ).
cnf(t2154,plain,
add(multiply(X1,X2),add(multiply(X1,X3),additive_identity)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t229,t274]) ).
cnf(t2155,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t2154,t257]) ).
cnf(t298,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t2155]) ).
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(f17,hypothesis,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f17_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
product(X0,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t4,plain,
multiply(X1,X1) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi2,hi17]) ).
cnf(t263,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t301,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t298,t263]) ).
cnf(t1430,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(orient,[status(thm)],[t301]) ).
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(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(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(t235,plain,
add(multiply(X1,additive_identity),multiply(X1,multiply(X2,X3))) = multiply(multiply(X1,X2),X3),
inference(hyper_resolution,[status(thm)],[hi16,h6,h15]) ).
cnf(t2157,plain,
multiply(X1,add(additive_identity,multiply(X2,X3))) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t235,t298]) ).
cnf(t2158,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(step,[status(thm)],[t2157,t258]) ).
cnf(t306,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t2158]) ).
cnf(t308,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t306,t263]) ).
cnf(t1108,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t308]) ).
cnf(t1118,plain,
multiply(X1,add(X2,multiply(X1,X3))) = add(multiply(X1,X2),multiply(X1,X3)),
inference(cp,[status(thm)],[t298,t1108]) ).
cnf(t2197,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t1118,t298]) ).
cnf(t1934,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t2197]) ).
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(t230,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(t2152,plain,
add(multiply(X1,X2),add(multiply(X3,X2),additive_identity)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t230,t274]) ).
cnf(t2153,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(step,[status(thm)],[t2152,t257]) ).
cnf(t292,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t2153]) ).
cnf(t294,plain,
multiply(add(X1,X2),X1) = add(X1,multiply(X2,X1)),
inference(cp,[status(thm)],[t292,t263]) ).
cnf(t1388,plain,
add(X1,multiply(X2,X1)) = multiply(add(X1,X2),X1),
inference(orient,[status(thm)],[t294]) ).
cnf(t1937,plain,
multiply(X1,add(X2,X2)) = multiply(X1,multiply(add(X2,X1),X2)),
inference(cp,[status(thm)],[t1934,t1388]) ).
cnf(t1993,plain,
multiply(X1,multiply(add(X2,X1),X2)) = multiply(X1,add(X2,X2)),
inference(orient,[status(thm)],[t1937]) ).
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(t29,plain,
add(X1,add(additive_identity,additive_inverse(X1))) = additive_identity,
inference(hyper_resolution,[status(thm)],[hi15,hi5,h21]) ).
cnf(t2151,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t29,t258]) ).
cnf(t288,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t2151]) ).
cnf(t1998,plain,
multiply(additive_inverse(X1),add(X1,X1)) = multiply(additive_inverse(X1),multiply(additive_identity,X1)),
inference(cp,[status(thm)],[t1993,t288]) ).
cnf(t290,plain,
add(X1,add(additive_inverse(X1),X2)) = add(additive_identity,X2),
inference(cp,[status(thm)],[t274,t288]) ).
cnf(t2172,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t290,t258]) ).
cnf(t1124,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t2172]) ).
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(t73,plain,
add(multiply(additive_identity,X1),multiply(X1,X1)) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi17,h11]) ).
cnf(t262,plain,
add(multiply(additive_identity,X1),multiply(X1,X1)) = X1,
inference(orient,[status(thm)],[t73]) ).
cnf(t2146,plain,
add(multiply(additive_identity,X1),X1) = X1,
inference(step,[status(thm)],[t262,t263]) ).
cnf(t265,plain,
add(multiply(additive_identity,X1),X1) = X1,
inference(rw,[status(thm)],[t2146]) ).
cnf(h20,plain,
sum(add(V0,additive_identity),V1,add(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi0,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(t56,plain,
add(X1,add(X2,additive_identity)) = add(X2,X1),
inference(hyper_resolution,[status(thm)],[hi15,h17,h20]) ).
cnf(t2149,plain,
add(X1,X2) = add(X2,X1),
inference(step,[status(thm)],[t56,t257]) ).
cnf(t273,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t2149]) ).
cnf(t2171,plain,
add(X1,multiply(additive_identity,X1)) = X1,
inference(step,[status(thm)],[t265,t273]) ).
cnf(t1093,plain,
add(X1,multiply(additive_identity,X1)) = X1,
inference(orient,[status(thm)],[t2171]) ).
cnf(t1127,plain,
multiply(additive_identity,additive_inverse(X1)) = add(X1,additive_inverse(X1)),
inference(cp,[status(thm)],[t1124,t1093]) ).
cnf(t2176,plain,
multiply(additive_identity,additive_inverse(X1)) = additive_identity,
inference(step,[status(thm)],[t1127,t288]) ).
cnf(t1162,plain,
multiply(additive_identity,additive_inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t2176]) ).
cnf(t1128,plain,
additive_inverse(additive_inverse(X1)) = add(X1,additive_identity),
inference(cp,[status(thm)],[t1124,t288]) ).
cnf(t2173,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(step,[status(thm)],[t1128,t257]) ).
cnf(t1144,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2173]) ).
cnf(t1163,plain,
additive_identity = multiply(additive_identity,X1),
inference(cp,[status(thm)],[t1162,t1144]) ).
cnf(t1170,plain,
multiply(additive_identity,X1) = additive_identity,
inference(orient,[status(thm)],[t1163]) ).
cnf(t2198,plain,
multiply(additive_inverse(X1),add(X1,X1)) = multiply(additive_inverse(X1),additive_identity),
inference(step,[status(thm)],[t1998,t1170]) ).
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(t70,plain,
add(multiply(X1,X1),multiply(X1,additive_identity)) = X1,
inference(hyper_resolution,[status(thm)],[hi16,hi17,h14]) ).
cnf(t259,plain,
add(multiply(X1,X1),multiply(X1,additive_identity)) = X1,
inference(orient,[status(thm)],[t70]) ).
cnf(t2145,plain,
add(X1,multiply(X1,additive_identity)) = X1,
inference(step,[status(thm)],[t259,t263]) ).
cnf(t264,plain,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[t2145]) ).
cnf(t1079,plain,
add(X1,multiply(X1,additive_identity)) = X1,
inference(orient,[status(thm)],[t264]) ).
cnf(t1126,plain,
multiply(additive_inverse(X1),additive_identity) = add(X1,additive_inverse(X1)),
inference(cp,[status(thm)],[t1124,t1079]) ).
cnf(t2174,plain,
multiply(additive_inverse(X1),additive_identity) = additive_identity,
inference(step,[status(thm)],[t1126,t288]) ).
cnf(t1147,plain,
multiply(additive_inverse(X1),additive_identity) = additive_identity,
inference(orient,[status(thm)],[t2174]) ).
cnf(t2199,plain,
multiply(additive_inverse(X1),add(X1,X1)) = additive_identity,
inference(step,[status(thm)],[t2198,t1147]) ).
cnf(t2023,plain,
multiply(additive_inverse(X1),add(X1,X1)) = additive_identity,
inference(orient,[status(thm)],[t2199]) ).
cnf(t2031,plain,
multiply(additive_inverse(X1),add(additive_inverse(X1),add(X1,X1))) = add(additive_inverse(X1),additive_identity),
inference(cp,[status(thm)],[t1430,t2023]) ).
cnf(t1130,plain,
X1 = add(X2,add(X1,additive_inverse(X2))),
inference(cp,[status(thm)],[t1124,t273]) ).
cnf(t1220,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(orient,[status(thm)],[t1130]) ).
cnf(t1223,plain,
X1 = add(additive_inverse(X2),add(X1,X2)),
inference(cp,[status(thm)],[t1220,t1144]) ).
cnf(t1260,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(orient,[status(thm)],[t1223]) ).
cnf(t2200,plain,
multiply(additive_inverse(X1),X1) = add(additive_inverse(X1),additive_identity),
inference(step,[status(thm)],[t2031,t1260]) ).
cnf(t2201,plain,
multiply(additive_inverse(X1),X1) = additive_inverse(X1),
inference(step,[status(thm)],[t2200,t257]) ).
cnf(t2040,plain,
multiply(additive_inverse(X1),X1) = additive_inverse(X1),
inference(orient,[status(thm)],[t2201]) ).
cnf(t2043,plain,
additive_inverse(additive_inverse(X1)) = multiply(X1,additive_inverse(X1)),
inference(cp,[status(thm)],[t2040,t1144]) ).
cnf(t2202,plain,
X1 = multiply(X1,additive_inverse(X1)),
inference(step,[status(thm)],[t2043,t1144]) ).
cnf(t2054,plain,
multiply(X1,additive_inverse(X1)) = X1,
inference(orient,[status(thm)],[t2202]) ).
cnf(t2058,plain,
multiply(X1,add(X1,additive_inverse(X1))) = add(X1,X1),
inference(cp,[status(thm)],[t1430,t2054]) ).
cnf(t2203,plain,
multiply(X1,additive_identity) = add(X1,X1),
inference(step,[status(thm)],[t2058,t288]) ).
cnf(t1148,plain,
additive_identity = multiply(X1,additive_identity),
inference(cp,[status(thm)],[t1147,t1144]) ).
cnf(t1156,plain,
multiply(X1,additive_identity) = additive_identity,
inference(orient,[status(thm)],[t1148]) ).
cnf(t2204,plain,
additive_identity = add(X1,X1),
inference(step,[status(thm)],[t2203,t1156]) ).
cnf(t2069,plain,
add(X1,X1) = additive_identity,
inference(orient,[status(thm)],[t2204]) ).
cnf(t2080,plain,
true = sum(X1,X1,additive_identity),
inference(cp,[status(thm)],[t366,t2069]) ).
cnf(t2125,plain,
sum(X1,X1,additive_identity) = true,
inference(orient,[status(thm)],[t2080]) ).
cnf(f18,negated_conjecture,
~ sum(a,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_a_is_id) ).
fof(f18_nnf,plain,
~ sum(a,a,additive_identity),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
~ sum(a,a,additive_identity),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
~ sum(a,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
sum(a,a,additive_identity) != true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2125]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/5.45 % Computer : n017.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Thu Sep 24 07:37:52 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 33.00/9.73 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.00/9.73 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------