%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 25.83s 3.84s
% Output : CNFRefutation 26.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of formulae : 126 ( 79 unt; 0 def)
% Number of atoms : 226 ( 43 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 202 ( 102 ~; 100 |; 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 : 325 ( 325 !; 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(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,axiom,
! [X] : product(X,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product(additive_identity,X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,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(f39,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)],[f38]) ).
fof(f42,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(f43,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)],[f42]) ).
fof(f44,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(f45,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)],[f44]) ).
fof(f46,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f51,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f49,f53]) ).
fof(f88,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f25,f55]) ).
fof(f103,plain,
! [X0,X1,X2,X3] :
( sum(additive_inverse(X0),X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4] :
( sum(X3,X2,X4)
| ~ sum(add(X3,X0),X1,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f117,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f183,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f185,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f47,f24]) ).
fof(f186,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f117]) ).
fof(f187,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f191,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f183,f117]) ).
fof(f231,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f186,f26]) ).
fof(f238,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)],[f39,f52]) ).
fof(f251,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(multiply(X3,X1),X2,X5)
| ~ product(X4,X1,X5)
| ~ sum(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f43,f25]) ).
fof(f252,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)],[f43,f52]) ).
fof(f542,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)],[f45,f52]) ).
fof(f553,plain,
! [X0,X1] :
( sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f103,f27]) ).
fof(f557,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f103,f117]) ).
fof(f599,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X0,X1),X3)
| ~ product(X0,X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f238,f25]) ).
fof(f815,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X1,X0),X3)
| ~ product(X2,X0,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f252,f25]) ).
fof(f982,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X2,X1),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f107,f117]) ).
fof(f983,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X1,X2),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f107,f26]) ).
fof(f1131,plain,
! [X0,X1,X2,X3] :
( product(X2,X0,X3)
| ~ sum(X0,multiply(X1,X0),X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f542,f25]) ).
fof(f3123,plain,
! [X0,X1,X2,X3] :
( sum(multiply(X0,X1),X1,X3)
| ~ product(X2,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f251,f52]) ).
fof(f3217,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f553,f23]) ).
fof(f3232,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(resolution,[status(thm)],[f3217,f185]) ).
fof(f3414,plain,
! [X0,X1] :
( sum(X0,multiply(X0,additive_inverse(X0)),X1)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f599,f28]) ).
fof(f3416,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(resolution,[status(thm)],[f599,f117]) ).
fof(f3417,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(resolution,[status(thm)],[f599,f26]) ).
fof(f3494,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f557,f23]) ).
fof(f3516,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f3494,f187]) ).
fof(f3536,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f3232,f3516]) ).
fof(f3538,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X0) = additive_inverse(X1),
inference(paramodulation,[status(thm)],[f3516,f3516]) ).
fof(f3542,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f231,f3516]) ).
fof(f3558,plain,
! [X0,X1] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f231,f3538]) ).
fof(f3947,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f231,f3536]) ).
fof(f4000,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X1) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f3542,f3516]) ).
fof(f4019,plain,
! [X0,X1] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f231,f4000]) ).
fof(f5392,plain,
! [X0,X1,X2] :
( sum(X1,multiply(X0,X1),X2)
| ~ product(add(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f815,f117]) ).
fof(f5393,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X1,X0),X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(resolution,[status(thm)],[f815,f26]) ).
fof(f6153,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(X1,add(X0,X2))),
inference(resolution,[status(thm)],[f982,f117]) ).
fof(f6193,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X0,X1),X2)),
inference(resolution,[status(thm)],[f983,f26]) ).
fof(f6488,plain,
! [X0,X1,X2] :
( product(add(X1,X0),X0,X2)
| ~ sum(X0,multiply(X1,X0),X2) ),
inference(resolution,[status(thm)],[f1131,f117]) ).
fof(f6553,plain,
! [X0] : sum(X0,multiply(X0,additive_inverse(X0)),additive_identity),
inference(resolution,[status(thm)],[f3414,f50]) ).
fof(f6608,plain,
! [X0] : add(X0,multiply(X0,additive_inverse(X0))) = additive_identity,
inference(resolution,[status(thm)],[f6553,f187]) ).
fof(f6651,plain,
! [X0] : add(X0,additive_identity) = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f6608,f3947]) ).
fof(f6707,plain,
! [X0] : X0 = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f191,f6651]) ).
fof(f6708,plain,
! [X0] : X0 = multiply(additive_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f3232,f6707]) ).
fof(f9235,plain,
! [X0,X1] :
( sum(multiply(additive_inverse(X0),X0),X0,X1)
| ~ product(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f3123,f27]) ).
fof(f9249,plain,
! [X0,X1] :
( sum(X0,X0,X1)
| ~ product(additive_identity,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f6708,f9235]) ).
fof(f9259,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(resolution,[status(thm)],[f9249,f51]) ).
fof(f9350,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(resolution,[status(thm)],[f9259,f187]) ).
fof(f9412,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f9350,f3947]) ).
fof(f9488,plain,
! [X0] : X0 = additive_inverse(X0),
inference(forward_demodulation,[status(thm)],[f191,f9412]) ).
fof(f9552,plain,
! [X0,X1] : add(X0,add(X1,X0)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f9488,f4019]) ).
fof(f9556,plain,
! [X0,X1] : add(X0,add(X0,X1)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f9488,f3558]) ).
fof(f9637,plain,
! [X0,X1] : add(X0,add(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f9488,f9552]) ).
fof(f9641,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f9488,f9556]) ).
fof(f10720,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X1,X0))),
inference(resolution,[status(thm)],[f3416,f25]) ).
fof(f10750,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X0,X1))),
inference(resolution,[status(thm)],[f3417,f25]) ).
fof(f11372,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X2,X1)),
inference(resolution,[status(thm)],[f6153,f186]) ).
fof(f11844,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(resolution,[status(thm)],[f6193,f187]) ).
fof(f13795,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(resolution,[status(thm)],[f10720,f187]) ).
fof(f14087,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[f10750,f187]) ).
fof(f17516,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X1,X0),X0)),
inference(resolution,[status(thm)],[f5392,f25]) ).
fof(f17534,plain,
! [X0,X1] : sum(X0,multiply(X1,X0),multiply(add(X0,X1),X0)),
inference(resolution,[status(thm)],[f5393,f25]) ).
fof(f20094,plain,
! [X0,X1] : product(add(X0,X1),X1,add(multiply(X0,X1),X1)),
inference(resolution,[status(thm)],[f6488,f117]) ).
fof(f20122,plain,
! [X0,X1] : product(add(X0,X1),X1,add(X1,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f231,f20094]) ).
fof(f21351,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(forward_demodulation,[status(thm)],[f11372,f11844]) ).
fof(f28261,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f13795,f14087]) ).
fof(f34669,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X1,X0),X0),
inference(resolution,[status(thm)],[f17516,f187]) ).
fof(f34893,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(resolution,[status(thm)],[f17534,f187]) ).
fof(f35913,plain,
! [X0,X1] : product(X0,add(X0,X1),add(add(X0,X1),multiply(X1,add(X0,X1)))),
inference(paramodulation,[status(thm)],[f9637,f20122]) ).
fof(f36012,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(multiply(X1,add(X0,X1)),X1))),
inference(forward_demodulation,[status(thm)],[f11372,f35913]) ).
fof(f36013,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(X1,multiply(X1,add(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f21351,f36012]) ).
fof(f36014,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(add(X0,X1),X1)))),
inference(forward_demodulation,[status(thm)],[f13795,f36013]) ).
fof(f36015,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(X1,add(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f28261,f36014]) ).
fof(f36016,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f9637,f36015]) ).
fof(f44310,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = multiply(add(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f34669,f34893]) ).
fof(f45351,plain,
! [X0,X1] : product(X0,add(X0,X1),multiply(add(X1,X0),X0)),
inference(forward_demodulation,[status(thm)],[f34669,f36016]) ).
fof(f45473,plain,
! [X0,X1] : product(X0,X1,multiply(add(add(X0,X1),X0),X0)),
inference(paramodulation,[status(thm)],[f9641,f45351]) ).
fof(f45559,plain,
! [X0,X1] : product(X0,X1,multiply(add(X0,add(X0,X1)),X0)),
inference(forward_demodulation,[status(thm)],[f44310,f45473]) ).
fof(f45560,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f9641,f45559]) ).
fof(f46081,plain,
product(b,a,c),
inference(paramodulation,[status(thm)],[f88,f45560]) ).
fof(f46173,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f46081,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG008-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n018.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 04:13:02 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Drodi V4.1.1
% 25.83/3.84 % Refutation found
% 25.83/3.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 25.83/3.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.71/3.89 % Elapsed time: 3.456616 seconds
% 26.71/3.89 % CPU time: 27.014546 seconds
% 26.71/3.89 % Total memory used: 115.962 MB
% 26.71/3.89 % Net memory used: 100.843 MB
%------------------------------------------------------------------------------