%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 76.18s 10.10s
% Output : CNFRefutation 43.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 134 ( 76 unt; 0 def)
% Number of atoms : 258 ( 46 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 250 ( 126 ~; 124 |; 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(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(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(f10,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,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,axiom,
! [X,Y,Z,W] :
( Y = W
| ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ),
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(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(f34,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
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,
! [Y,W] :
( Y = W
| ! [X,Z] :
( ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
~ product(b,a,c),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f49,f55]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f49,f54]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( product(X0,X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f35,f54]) ).
fof(f76,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,f54]) ).
fof(f80,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f25,f57]) ).
fof(f82,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(multiply(X0,X3),X2,X5)
| ~ product(X0,X4,X5)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f39]) ).
fof(f84,plain,
! [X0,X1,X2] :
( product(X0,multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f60]) ).
fof(f85,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f25,f58]) ).
fof(f95,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f101,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(f106,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(f140,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(f141,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,f54]) ).
fof(f149,plain,
! [X0,X1] : product(X0,multiply(X0,X1),multiply(X0,X1)),
inference(resolution,[status(thm)],[f84,f25]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X4,X1,X5)
| ~ sum(multiply(X3,X1),X2,X5)
| ~ sum(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f216,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f219,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f95]) ).
fof(f220,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f224,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f216,f95]) ).
fof(f264,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f219,f26]) ).
fof(f285,plain,
! [X0,X1] :
( additive_identity = X1
| ~ sum(X0,X1,X0) ),
inference(resolution,[status(thm)],[f51,f24]) ).
fof(f287,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ sum(X0,X1,add(X0,X2)) ),
inference(resolution,[status(thm)],[f51,f26]) ).
fof(f378,plain,
! [X0,X1,X2,X3] :
( sum(X0,multiply(X0,X1),X3)
| ~ product(X0,X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f76,f25]) ).
fof(f386,plain,
! [X0,X1,X2,X3,X4] :
( sum(multiply(X3,X0),multiply(X3,X1),X4)
| ~ product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f82,f25]) ).
fof(f477,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f101,f95]) ).
fof(f478,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X2,X0),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f101,f26]) ).
fof(f912,plain,
! [X0,X1,X2,X3] :
( sum(multiply(X0,X1),X1,X3)
| ~ product(X2,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f140,f54]) ).
fof(f924,plain,
! [X0,X1,X2] :
( sum(X0,X0,X2)
| ~ product(X1,X0,X2)
| ~ sum(X0,X0,X1) ),
inference(resolution,[status(thm)],[f141,f54]) ).
fof(f1005,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X2,X1),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f106,f95]) ).
fof(f1006,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X1,X2),X3)
| ~ sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f106,f26]) ).
fof(f1046,plain,
! [X0,X1] :
( sum(X0,X0,X1)
| ~ product(add(X0,X0),X0,X1) ),
inference(resolution,[status(thm)],[f924,f95]) ).
fof(f1048,plain,
! [X0] : sum(X0,X0,multiply(add(X0,X0),X0)),
inference(resolution,[status(thm)],[f1046,f25]) ).
fof(f1067,plain,
! [X0] : add(X0,X0) = multiply(add(X0,X0),X0),
inference(resolution,[status(thm)],[f1048,f220]) ).
fof(f1098,plain,
! [X0,X1,X2,X3] :
( product(X2,X1,X3)
| ~ sum(multiply(X0,X1),X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f210,f54]) ).
fof(f1773,plain,
! [X0,X1] :
( sum(X0,multiply(X0,additive_identity),X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f378,f24]) ).
fof(f1774,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X1,X0),X2) ),
inference(resolution,[status(thm)],[f378,f95]) ).
fof(f1775,plain,
! [X0,X1,X2] :
( sum(X0,multiply(X0,X1),X2)
| ~ product(X0,add(X0,X1),X2) ),
inference(resolution,[status(thm)],[f378,f26]) ).
fof(f1864,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),multiply(X0,X0)),
inference(resolution,[status(thm)],[f1773,f25]) ).
fof(f1866,plain,
! [X0] : sum(X0,multiply(X0,additive_identity),X0),
inference(forward_demodulation,[status(thm)],[f85,f1864]) ).
fof(f1868,plain,
! [X0,X1,X2] :
( sum(multiply(X0,additive_inverse(X2)),multiply(X0,X2),X1)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f386,f27]) ).
fof(f1938,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(resolution,[status(thm)],[f1866,f285]) ).
fof(f1986,plain,
! [X0] : product(X0,multiply(X0,additive_identity),additive_identity),
inference(paramodulation,[status(thm)],[f1938,f149]) ).
fof(f2004,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f1938,f1986]) ).
fof(f2105,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f477,f23]) ).
fof(f2116,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
inference(resolution,[status(thm)],[f478,f23]) ).
fof(f2465,plain,
! [X0,X1] : X0 = add(add(additive_inverse(X1),X0),X1),
inference(resolution,[status(thm)],[f2105,f287]) ).
fof(f2485,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f2105,f220]) ).
fof(f2501,plain,
! [X0,X1] : X0 = add(X1,add(additive_inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f264,f2465]) ).
fof(f2536,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(resolution,[status(thm)],[f2116,f220]) ).
fof(f2687,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X0) = additive_inverse(X1),
inference(paramodulation,[status(thm)],[f2485,f2485]) ).
fof(f2722,plain,
! [X0,X1] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f264,f2687]) ).
fof(f4229,plain,
! [X0,X1,X2] :
( sum(multiply(X1,X0),X0,X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(resolution,[status(thm)],[f912,f95]) ).
fof(f4506,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(X1,add(X0,X2))),
inference(resolution,[status(thm)],[f1005,f95]) ).
fof(f4535,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X0,X1),X2)),
inference(resolution,[status(thm)],[f1006,f26]) ).
fof(f5063,plain,
! [X0,X1,X2] :
( product(add(X1,X0),X1,X2)
| ~ sum(multiply(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f1098,f95]) ).
fof(f7893,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X1,X0))),
inference(resolution,[status(thm)],[f1774,f25]) ).
fof(f7914,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),multiply(X0,add(X0,X1))),
inference(resolution,[status(thm)],[f1775,f25]) ).
fof(f8228,plain,
! [X0,X1] : sum(multiply(X0,additive_inverse(X1)),multiply(X0,X1),additive_identity),
inference(resolution,[status(thm)],[f1868,f2004]) ).
fof(f9974,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,X0)),
inference(resolution,[status(thm)],[f7893,f220]) ).
fof(f10149,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(resolution,[status(thm)],[f7914,f220]) ).
fof(f10406,plain,
! [X0,X1] : add(multiply(X0,additive_inverse(X1)),multiply(X0,X1)) = additive_identity,
inference(resolution,[status(thm)],[f8228,f220]) ).
fof(f10470,plain,
! [X0,X1] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = additive_identity,
inference(forward_demodulation,[status(thm)],[f264,f10406]) ).
fof(f11826,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = multiply(X0,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f9974,f10149]) ).
fof(f12260,plain,
! [X0] : add(add(X0,X0),multiply(add(X0,X0),additive_inverse(X0))) = additive_identity,
inference(paramodulation,[status(thm)],[f1067,f10470]) ).
fof(f12386,plain,
! [X0] : multiply(add(X0,X0),add(additive_inverse(X0),add(X0,X0))) = additive_identity,
inference(forward_demodulation,[status(thm)],[f9974,f12260]) ).
fof(f12387,plain,
! [X0] : multiply(add(X0,X0),X0) = additive_identity,
inference(forward_demodulation,[status(thm)],[f2536,f12386]) ).
fof(f12388,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(forward_demodulation,[status(thm)],[f1067,f12387]) ).
fof(f12616,plain,
! [X0] : additive_inverse(X0) = add(X0,additive_identity),
inference(paramodulation,[status(thm)],[f12388,f2501]) ).
fof(f12725,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[status(thm)],[f224,f12616]) ).
fof(f12829,plain,
! [X0,X1] : add(X0,add(X0,X1)) = additive_inverse(X1),
inference(backward_demodulation,[status(thm)],[f12725,f2722]) ).
fof(f12958,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f12725,f12829]) ).
fof(f14141,plain,
! [X0,X1] : sum(multiply(X0,X1),X1,multiply(add(X1,X0),X1)),
inference(resolution,[status(thm)],[f4229,f25]) ).
fof(f14809,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X2,X1)),
inference(resolution,[status(thm)],[f4506,f219]) ).
fof(f15296,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(resolution,[status(thm)],[f4535,f220]) ).
fof(f15831,plain,
! [X0,X1] : product(add(X0,X1),X0,add(X0,multiply(X1,X0))),
inference(resolution,[status(thm)],[f5063,f95]) ).
fof(f22510,plain,
! [X0,X1] : add(multiply(X0,X1),X1) = multiply(add(X1,X0),X1),
inference(resolution,[status(thm)],[f14141,f220]) ).
fof(f22599,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f264,f22510]) ).
fof(f29790,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X0,add(X2,X1)),
inference(forward_demodulation,[status(thm)],[f14809,f15296]) ).
fof(f30735,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)],[f11826,f15831]) ).
fof(f30824,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)],[f14809,f30735]) ).
fof(f30825,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)],[f12388,f30824]) ).
fof(f30826,plain,
! [X0,X1] : product(X0,add(X0,X1),add(add(X0,X1),multiply(X1,add(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f224,f30825]) ).
fof(f30827,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(multiply(X1,add(X1,X0)),X1))),
inference(forward_demodulation,[status(thm)],[f14809,f30826]) ).
fof(f30828,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,add(X1,multiply(X1,add(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f29790,f30827]) ).
fof(f30829,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(add(X1,X0),X1)))),
inference(forward_demodulation,[status(thm)],[f9974,f30828]) ).
fof(f30830,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,add(X1,add(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f11826,f30829]) ).
fof(f30831,plain,
! [X0,X1] : product(X0,add(X0,X1),add(X0,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f12958,f30830]) ).
fof(f57459,plain,
! [X0,X1] : product(X0,add(X0,X1),multiply(add(X0,X1),X0)),
inference(forward_demodulation,[status(thm)],[f22599,f30831]) ).
fof(f57565,plain,
! [X0,X1] : product(X0,X1,multiply(add(X0,add(X0,X1)),X0)),
inference(paramodulation,[status(thm)],[f12958,f57459]) ).
fof(f57637,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f12958,f57565]) ).
fof(f57869,plain,
product(b,a,c),
inference(paramodulation,[status(thm)],[f80,f57637]) ).
fof(f57938,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f57869,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-2 : 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 : n004.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 04:10:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 76.18/10.10 % Refutation found
% 76.18/10.10 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 76.18/10.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 43.53/10.15 % Elapsed time: 9.765016 seconds
% 43.53/10.15 % CPU time: 77.167074 seconds
% 43.53/10.15 % Total memory used: 233.344 MB
% 43.53/10.15 % Net memory used: 193.895 MB
%------------------------------------------------------------------------------