%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 81.41s 10.78s
% Output : CNFRefutation 81.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 142 ( 78 unt; 0 def)
% Number of atoms : 256 ( 35 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 230 ( 116 ~; 114 |; 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 : 374 ( 374 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,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(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(f19,axiom,
! [X] : sum(additive_inverse(additive_inverse(X)),additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] : sum(additive_inverse(X),additive_inverse(Y),additive_inverse(add(X,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y] : product(X,additive_inverse(Y),additive_inverse(multiply(X,Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f32,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f37,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,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(f43,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)],[f42]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f48,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(f49,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)],[f48]) ).
fof(f50,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f55,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f57,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f58,plain,
! [X0,X1] : sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X0,X1))),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f59,plain,
! [X0,X1] : product(X0,additive_inverse(X1),additive_inverse(multiply(X0,X1))),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f60,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f61,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f62,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f63,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f53,f61]) ).
fof(f64,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f53,f60]) ).
fof(f96,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f29,f63]) ).
fof(f101,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f29,f64]) ).
fof(f103,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f29,f53]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( sum(additive_inverse(X0),X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f31]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4] :
( sum(X3,X2,X4)
| ~ sum(add(X3,X0),X1,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f30]) ).
fof(f125,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f37,f30]) ).
fof(f190,plain,
! [X0] : sum(additive_identity,additive_inverse(additive_inverse(X0)),X0),
inference(resolution,[status(thm)],[f55,f37]) ).
fof(f199,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f51,f27]) ).
fof(f202,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f51,f125]) ).
fof(f203,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f51,f30]) ).
fof(f204,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(resolution,[status(thm)],[f199,f190]) ).
fof(f208,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f199,f125]) ).
fof(f241,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)],[f43,f60]) ).
fof(f255,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)],[f47,f60]) ).
fof(f400,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f202,f30]) ).
fof(f453,plain,
! [X0] : product(X0,additive_inverse(X0),additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f101,f59]) ).
fof(f486,plain,
! [X0] : product(additive_inverse(X0),X0,additive_inverse(additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f204,f453]) ).
fof(f495,plain,
! [X0] : product(additive_inverse(X0),X0,X0),
inference(forward_demodulation,[status(thm)],[f204,f486]) ).
fof(f508,plain,
! [X0] : multiply(additive_inverse(X0),X0) = X0,
inference(resolution,[status(thm)],[f495,f103]) ).
fof(f525,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)],[f49,f60]) ).
fof(f531,plain,
! [X0,X1] : sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X1,X0))),
inference(resolution,[status(thm)],[f58,f37]) ).
fof(f711,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X0,X1),X3)
| ~ product(X0,X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f241,f29]) ).
fof(f764,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f111,f125]) ).
fof(f1044,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X1,X0),X3)
| ~ product(X2,X0,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f255,f29]) ).
fof(f1160,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X2,X1),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f115,f125]) ).
fof(f1161,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X1,X2),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f115,f30]) ).
fof(f1713,plain,
! [X0,X1,X2,X3] :
( product(X2,X0,X3)
| ~ sum(X0,multiply(X1,X0),X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f525,f29]) ).
fof(f6721,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(additive_inverse(X0),additive_inverse(add(X1,X0)),X2) ),
inference(resolution,[status(thm)],[f711,f531]) ).
fof(f6722,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(additive_inverse(X0),additive_inverse(add(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f711,f58]) ).
fof(f6990,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f764,f27]) ).
fof(f7125,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f6990,f203]) ).
fof(f7164,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f204,f7125]) ).
fof(f7399,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f400,f7164]) ).
fof(f9163,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X1),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(additive_inverse(add(X0,X1)),additive_inverse(X1),X2) ),
inference(resolution,[status(thm)],[f1044,f531]) ).
fof(f9164,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X1),additive_inverse(X0)),X2)
| ~ product(additive_inverse(add(X0,X1)),additive_inverse(X0),X2) ),
inference(resolution,[status(thm)],[f1044,f58]) ).
fof(f9170,plain,
! [X0,X1] :
( sum(X0,multiply(additive_inverse(X0),X0),X1)
| ~ product(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f1044,f32]) ).
fof(f9180,plain,
! [X0,X1] :
( sum(X0,X0,X1)
| ~ product(additive_identity,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f508,f9170]) ).
fof(f9222,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(resolution,[status(thm)],[f9180,f57]) ).
fof(f9290,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(resolution,[status(thm)],[f9222,f203]) ).
fof(f9323,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f9290,f7399]) ).
fof(f9380,plain,
! [X0] : X0 = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f208,f9323]) ).
fof(f9478,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f9380,f7399]) ).
fof(f9490,plain,
! [X0,X1] : add(X0,add(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f9380,f7164]) ).
fof(f9980,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(X1,add(X0,X2))),
inference(resolution,[status(thm)],[f1160,f125]) ).
fof(f10120,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X0,X1),X2)),
inference(resolution,[status(thm)],[f1161,f30]) ).
fof(f10287,plain,
! [X0,X1,X2] :
( product(add(X0,X1),X0,X2)
| ~ sum(X0,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[f1713,f30]) ).
fof(f11307,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X2,X1)),
inference(resolution,[status(thm)],[f9980,f202]) ).
fof(f11968,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(resolution,[status(thm)],[f10120,f203]) ).
fof(f20288,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(forward_demodulation,[status(thm)],[f11307,f11968]) ).
fof(f27735,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(X0,additive_inverse(add(X1,X0)),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f6721]) ).
fof(f27736,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27735]) ).
fof(f27737,plain,
! [X0,X1,X2] :
( sum(X0,multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27736]) ).
fof(f27738,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,additive_inverse(X1)),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27737]) ).
fof(f27739,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27738]) ).
fof(f27742,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X1,X0))),
inference(resolution,[status(thm)],[f27739,f29]) ).
fof(f27768,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(X0,additive_inverse(add(X0,X1)),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f6722]) ).
fof(f27769,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27768]) ).
fof(f27770,plain,
! [X0,X1,X2] :
( sum(X0,multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27769]) ).
fof(f27771,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,additive_inverse(X1)),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27770]) ).
fof(f27772,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f27771]) ).
fof(f27775,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X0,X1))),
inference(resolution,[status(thm)],[f27772,f29]) ).
fof(f28505,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X1),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(add(X0,X1),additive_inverse(X1),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f9163]) ).
fof(f28506,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X1),multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(add(X0,X1),X1,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28505]) ).
fof(f28507,plain,
! [X0,X1,X2] :
( sum(X1,multiply(additive_inverse(X0),additive_inverse(X1)),X2)
| ~ product(add(X0,X1),X1,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28506]) ).
fof(f28508,plain,
! [X0,X1,X2] :
( sum(X1,multiply(X0,additive_inverse(X1)),X2)
| ~ product(add(X0,X1),X1,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28507]) ).
fof(f28509,plain,
! [X0,X1,X2] :
( sum(X1,multiply(X0,X1),X2)
| ~ product(add(X0,X1),X1,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28508]) ).
fof(f28511,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X1,X0),X0)),
inference(resolution,[status(thm)],[f28509,f29]) ).
fof(f28534,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X1),additive_inverse(X0)),X2)
| ~ product(add(X0,X1),additive_inverse(X0),X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f9164]) ).
fof(f28535,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X0),multiply(additive_inverse(X1),additive_inverse(X0)),X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28534]) ).
fof(f28536,plain,
! [X0,X1,X2] :
( sum(X0,multiply(additive_inverse(X1),additive_inverse(X0)),X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28535]) ).
fof(f28537,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X1,additive_inverse(X0)),X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28536]) ).
fof(f28538,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X1,X0),X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(forward_demodulation,[status(thm)],[f9380,f28537]) ).
fof(f28540,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X0,X1),X0)),
inference(resolution,[status(thm)],[f28538,f29]) ).
fof(f28672,plain,
! [X0,X1] : product(add(X0,X1),X0,add(multiply(X1,X0),X0)),
inference(resolution,[status(thm)],[f10287,f125]) ).
fof(f28697,plain,
! [X0,X1] : product(add(X0,X1),X0,add(X0,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f400,f28672]) ).
fof(f29614,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(resolution,[status(thm)],[f27742,f203]) ).
fof(f29808,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[f27775,f203]) ).
fof(f30534,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
inference(resolution,[status(thm)],[f28511,f203]) ).
fof(f30726,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(resolution,[status(thm)],[f28540,f203]) ).
fof(f33703,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f29614,f29808]) ).
fof(f33764,plain,
! [X0,X1] : product(add(add(X0,X1),X1),add(X0,X1),add(add(X0,X1),multiply(X1,add(X1,X0)))),
inference(paramodulation,[status(thm)],[f33703,f28697]) ).
fof(f33923,plain,
! [X0,X1] : product(add(X0,add(X1,X1)),add(X0,X1),add(add(X0,X1),multiply(X1,add(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f11307,f33764]) ).
fof(f33924,plain,
! [X0,X1] : product(add(X0,additive_identity),add(X0,X1),add(add(X0,X1),multiply(X1,add(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f9290,f33923]) ).
fof(f33925,plain,
! [X0,X1] : product(X0,add(X0,X1),add(add(X0,X1),multiply(X1,add(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f208,f33924]) ).
fof(f33926,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(multiply(X1,add(X1,X0)),X1))),
inference(forward_demodulation,[status(thm)],[f11307,f33925]) ).
fof(f33927,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(X1,multiply(X1,add(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f20288,f33926]) ).
fof(f33928,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(add(X1,X0),X1)))),
inference(forward_demodulation,[status(thm)],[f29614,f33927]) ).
fof(f33929,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(X1,add(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f33703,f33928]) ).
fof(f33930,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f9478,f33929]) ).
fof(f35417,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = multiply(add(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f30534,f30726]) ).
fof(f38291,plain,
! [X0,X1] : product(X0,add(X0,X1),multiply(add(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f30534,f33930]) ).
fof(f38381,plain,
! [X0,X1] : product(X0,X1,multiply(add(add(X1,X0),X0),X0)),
inference(paramodulation,[status(thm)],[f9490,f38291]) ).
fof(f38465,plain,
! [X0,X1] : product(X0,X1,multiply(add(X0,add(X1,X0)),X0)),
inference(forward_demodulation,[status(thm)],[f35417,f38381]) ).
fof(f38466,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f9490,f38465]) ).
fof(f38670,plain,
product(b,a,c),
inference(paramodulation,[status(thm)],[f96,f38466]) ).
fof(f38720,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f38670,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:11:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.03/0.38 % Drodi V4.1.1
% 81.41/10.78 % Refutation found
% 81.41/10.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 81.41/10.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.86/10.85 % Elapsed time: 10.457596 seconds
% 9.86/10.85 % CPU time: 82.236928 seconds
% 9.86/10.85 % Total memory used: 180.226 MB
% 9.86/10.85 % Net memory used: 152.449 MB
%------------------------------------------------------------------------------