%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:04:39 PM UTC 2026
% Result : Unsatisfiable 106.71s 14.00s
% Output : CNFRefutation 16.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 17
% Syntax : Number of formulae : 157 ( 101 unt; 0 def)
% Number of atoms : 270 ( 55 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 228 ( 115 ~; 113 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 386 ( 386 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X,V,W] :
( sum(X,V,W)
| ! [U,Z] :
( ~ sum(U,Z,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f34,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(V3,X,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X,V3,V4] :
( product(V3,X,V4)
| ! [V1,V2] :
( ~ sum(V1,V2,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f47,f49]) ).
fof(f52,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f47,f48]) ).
fof(f72,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f23,f51]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( product(multiply(X3,X0),X1,X4)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f23,f35]) ).
fof(f77,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f23,f52]) ).
fof(f79,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f23,f47]) ).
fof(f87,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( sum(additive_inverse(X0),X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4] :
( sum(X3,X2,X4)
| ~ sum(add(X3,X0),X1,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f24]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4] :
( sum(X0,X2,X4)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f75,f23]) ).
fof(f215,plain,
! [X0,X1] :
( additive_identity = X1
| ~ sum(additive_inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f216,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f45,f21]) ).
fof(f218,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f45,f22]) ).
fof(f219,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f87]) ).
fof(f220,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f224,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f216,f87]) ).
fof(f241,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(resolution,[status(thm)],[f215,f87]) ).
fof(f264,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f219,f24]) ).
fof(f293,plain,
! [X0,X1,X2,X3,X4] :
( sum(X1,X2,X4)
| ~ product(X3,X1,X4)
| ~ sum(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f41,f48]) ).
fof(f299,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X1,X4)
| ~ sum(X1,X2,X4)
| ~ sum(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f43,f48]) ).
fof(f415,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X0,X1),X3)
| ~ product(X0,X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f108,f23]) ).
fof(f508,plain,
! [X0,X1] :
( sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f93,f25]) ).
fof(f512,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f93,f87]) ).
fof(f513,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X2,X0),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f93,f24]) ).
fof(f571,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X1,X0),X3)
| ~ product(X2,X0,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f293,f23]) ).
fof(f738,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X2,X1),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f98,f87]) ).
fof(f739,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X1,X2),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f98,f24]) ).
fof(f862,plain,
! [X0,X1,X2,X3] :
( product(X2,X0,X3)
| ~ sum(X0,multiply(X1,X0),X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f299,f23]) ).
fof(f1251,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f207,f23]) ).
fof(f1472,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[f1251,f79]) ).
fof(f1475,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,multiply(X0,X1))),
inference(resolution,[status(thm)],[f1251,f52]) ).
fof(f1497,plain,
! [X0,X1] : product(multiply(multiply(X0,X1),X0),X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f77,f1251]) ).
fof(f1787,plain,
! [X0,X1] : product(X0,multiply(X1,multiply(X0,X1)),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f1475,f23]) ).
fof(f1857,plain,
! [X0,X1] : product(multiply(X0,multiply(X1,X0)),X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1472,f1497]) ).
fof(f2413,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f508,f21]) ).
fof(f2427,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(resolution,[status(thm)],[f2413,f218]) ).
fof(f2478,plain,
! [X0,X1] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),X0),X1)
| ~ product(additive_inverse(X0),additive_identity,X1) ),
inference(resolution,[status(thm)],[f415,f25]) ).
fof(f2482,plain,
! [X0,X1] :
( sum(X0,multiply(X0,additive_identity),X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f415,f22]) ).
fof(f2483,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(resolution,[status(thm)],[f415,f87]) ).
fof(f2484,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(resolution,[status(thm)],[f415,f24]) ).
fof(f2488,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),multiply(X0,X0)),
inference(resolution,[status(thm)],[f2482,f23]) ).
fof(f2492,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),X0),
inference(forward_demodulation,[status(thm)],[f77,f2488]) ).
fof(f2511,plain,
! [X0] : add(X0,multiply(X0,additive_identity)) = X0,
inference(resolution,[status(thm)],[f2492,f220]) ).
fof(f2740,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f512,f21]) ).
fof(f2754,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
inference(resolution,[status(thm)],[f513,f21]) ).
fof(f2886,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f2740,f220]) ).
fof(f2924,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(resolution,[status(thm)],[f2754,f220]) ).
fof(f2933,plain,
! [X0] : sum(additive_inverse(X0),X0,multiply(X0,additive_identity)),
inference(paramodulation,[status(thm)],[f2511,f2754]) ).
fof(f2947,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X0) = additive_inverse(X1),
inference(paramodulation,[status(thm)],[f2886,f2886]) ).
fof(f2969,plain,
! [X0,X1] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f264,f2947]) ).
fof(f3188,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(resolution,[status(thm)],[f2933,f215]) ).
fof(f3274,plain,
! [X0] : product(X0,multiply(additive_identity,multiply(X0,additive_identity)),additive_identity),
inference(paramodulation,[status(thm)],[f3188,f1787]) ).
fof(f3307,plain,
! [X0] : product(X0,multiply(additive_identity,additive_identity),additive_identity),
inference(forward_demodulation,[status(thm)],[f3188,f3274]) ).
fof(f3308,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f3188,f3307]) ).
fof(f3383,plain,
! [X0,X1] :
( sum(X0,multiply(additive_inverse(X0),X0),X1)
| ~ product(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f571,f26]) ).
fof(f3384,plain,
! [X0,X1] :
( sum(X0,multiply(additive_identity,X0),X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f571,f22]) ).
fof(f3385,plain,
! [X0,X1,X2] :
( sum(X1,multiply(X0,X1),X2)
| ~ product(add(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f571,f87]) ).
fof(f3386,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X1,X0),X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(resolution,[status(thm)],[f571,f24]) ).
fof(f3400,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f2427,f2924]) ).
fof(f3411,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X1) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f2924,f2886]) ).
fof(f3430,plain,
! [X0,X1] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f264,f3411]) ).
fof(f3640,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(X1,add(X0,X2))),
inference(resolution,[status(thm)],[f738,f87]) ).
fof(f3739,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X0,X1),X2)),
inference(resolution,[status(thm)],[f739,f24]) ).
fof(f3811,plain,
! [X0,X1,X2] :
( product(add(X1,X0),X0,X2)
| ~ sum(X0,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[f862,f87]) ).
fof(f4230,plain,
! [X0] : sum(X0,multiply(additive_identity,X0),multiply(X0,X0)),
inference(resolution,[status(thm)],[f3384,f23]) ).
fof(f4235,plain,
! [X0] : sum(X0,multiply(additive_identity,X0),X0),
inference(forward_demodulation,[status(thm)],[f77,f4230]) ).
fof(f4268,plain,
! [X0] : add(X0,multiply(additive_identity,X0)) = X0,
inference(resolution,[status(thm)],[f4235,f220]) ).
fof(f4355,plain,
! [X0] : add(additive_inverse(X0),X0) = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f4268,f2924]) ).
fof(f4377,plain,
! [X0] : add(X0,additive_inverse(X0)) = multiply(additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f264,f4355]) ).
fof(f4378,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f241,f4377]) ).
fof(f4415,plain,
! [X0] : product(additive_identity,X0,multiply(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f4378,f1857]) ).
fof(f4449,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f4378,f4415]) ).
fof(f6692,plain,
! [X0] : sum(additive_inverse(X0),multiply(additive_inverse(X0),X0),additive_identity),
inference(resolution,[status(thm)],[f2478,f3308]) ).
fof(f6819,plain,
! [X0] : sum(X0,multiply(additive_inverse(additive_inverse(X0)),additive_inverse(X0)),additive_identity),
inference(paramodulation,[status(thm)],[f2427,f6692]) ).
fof(f6839,plain,
! [X0] : sum(X0,multiply(X0,additive_inverse(X0)),additive_identity),
inference(forward_demodulation,[status(thm)],[f2427,f6819]) ).
fof(f6888,plain,
! [X0] : add(X0,multiply(X0,additive_inverse(X0))) = additive_identity,
inference(resolution,[status(thm)],[f6839,f220]) ).
fof(f6944,plain,
! [X0] : add(X0,additive_identity) = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f6888,f3400]) ).
fof(f7006,plain,
! [X0] : X0 = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f224,f6944]) ).
fof(f7007,plain,
! [X0] : X0 = multiply(additive_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f2427,f7006]) ).
fof(f7268,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X1,X0))),
inference(resolution,[status(thm)],[f2483,f23]) ).
fof(f7377,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X0,X1))),
inference(resolution,[status(thm)],[f2484,f23]) ).
fof(f8954,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(resolution,[status(thm)],[f7268,f220]) ).
fof(f9122,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[f7377,f220]) ).
fof(f9312,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X2,X1)),
inference(resolution,[status(thm)],[f3640,f219]) ).
fof(f9800,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(resolution,[status(thm)],[f3739,f220]) ).
fof(f10058,plain,
! [X0,X1] :
( sum(X0,X0,X1)
| ~ product(additive_identity,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f7007,f3383]) ).
fof(f10059,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(resolution,[status(thm)],[f10058,f4449]) ).
fof(f10084,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X1,X0),X0)),
inference(resolution,[status(thm)],[f3385,f23]) ).
fof(f10174,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(resolution,[status(thm)],[f10059,f220]) ).
fof(f10240,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f10174,f3400]) ).
fof(f10339,plain,
! [X0] : X0 = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f224,f10240]) ).
fof(f10423,plain,
! [X0,X1] : add(X0,add(X1,X0)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f10339,f3430]) ).
fof(f10427,plain,
! [X0,X1] : add(X0,add(X0,X1)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f10339,f2969]) ).
fof(f10511,plain,
! [X0,X1] : add(X0,add(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f10339,f10423]) ).
fof(f10515,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f10339,f10427]) ).
fof(f11360,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X0,X1),X0)),
inference(resolution,[status(thm)],[f3386,f23]) ).
fof(f11521,plain,
! [X0,X1] : product(add(X0,X1),X1,add(multiply(X0,X1),X1)),
inference(resolution,[status(thm)],[f3811,f87]) ).
fof(f11544,plain,
! [X0,X1] : product(add(X0,X1),X1,add(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f264,f11521]) ).
fof(f13387,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f8954,f9122]) ).
fof(f13737,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
inference(resolution,[status(thm)],[f10084,f220]) ).
fof(f18269,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(forward_demodulation,[status(thm)],[f9312,f9800]) ).
fof(f23900,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(resolution,[status(thm)],[f11360,f220]) ).
fof(f24106,plain,
! [X0,X1] : product(X0,add(X0,X1),add(add(X0,X1),multiply(X1,add(X0,X1)))),
inference(paramodulation,[status(thm)],[f10511,f11544]) ).
fof(f24205,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(multiply(X1,add(X0,X1)),X1))),
inference(forward_demodulation,[status(thm)],[f9312,f24106]) ).
fof(f24206,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(X1,multiply(X1,add(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f18269,f24205]) ).
fof(f24207,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(add(X0,X1),X1)))),
inference(forward_demodulation,[status(thm)],[f8954,f24206]) ).
fof(f24208,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(X1,add(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f13387,f24207]) ).
fof(f24209,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f10511,f24208]) ).
fof(f42123,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = multiply(add(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f13737,f23900]) ).
fof(f43101,plain,
! [X0,X1] : product(X0,add(X0,X1),multiply(add(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f13737,f24209]) ).
fof(f43203,plain,
! [X0,X1] : product(X0,X1,multiply(add(add(X0,X1),X0),X0)),
inference(paramodulation,[status(thm)],[f10515,f43101]) ).
fof(f43280,plain,
! [X0,X1] : product(X0,X1,multiply(add(X0,add(X0,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f42123,f43203]) ).
fof(f43281,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f10515,f43280]) ).
fof(f44142,plain,
product(b,a,c),
inference(paramodulation,[status(thm)],[f72,f43281]) ).
fof(f44195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f44142,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:05:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 106.71/14.00 % Refutation found
% 106.71/14.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 106.71/14.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 16.70/14.04 % Elapsed time: 13.656257 seconds
% 16.70/14.04 % CPU time: 107.520285 seconds
% 16.70/14.04 % Total memory used: 200.029 MB
% 16.70/14.04 % Net memory used: 166.672 MB
%------------------------------------------------------------------------------