%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:32:13 PM UTC 2026
% Result : Unsatisfiable 57.34s 7.66s
% Output : CNFRefutation 57.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 140 ( 95 unt; 0 def)
% Number of atoms : 209 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 141 ( 72 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 215 ( 215 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [X,Y] :
( product(X,Y,identity)
| ~ product(X,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
! [X,Y] :
( product(Y,X,identity)
| ~ product(X,X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
product(c,inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
product(d,inverse(b),h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
product(h,b,j),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
product(j,inverse(h),k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ product(k,inverse(b),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,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)],[f7]) ).
fof(f25,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)],[f24]) ).
fof(f26,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)],[f8]) ).
fof(f27,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)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( product(X0,X1,identity)
| ~ product(X0,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1] :
( product(X1,X0,identity)
| ~ product(X0,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,plain,
product(c,inverse(a),d),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
product(d,inverse(b),h),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f33,plain,
product(h,b,j),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
product(j,inverse(h),k),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f35,plain,
~ product(k,inverse(b),identity),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = X1
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f23,f17]) ).
fof(f44,plain,
! [X0] :
( d = X0
| ~ product(c,inverse(a),X0) ),
inference(resolution,[status(thm)],[f23,f31]) ).
fof(f46,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f23,f30]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f23,f18]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f52,plain,
! [X0,X1,X2] :
( product(d,X1,X2)
| ~ product(h,X0,X2)
| ~ product(inverse(b),X0,X1) ),
inference(resolution,[status(thm)],[f25,f32]) ).
fof(f53,plain,
! [X0,X1,X2] :
( product(c,X1,X2)
| ~ product(d,X0,X2)
| ~ product(inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f54,plain,
! [X0,X1,X2] :
( product(h,X1,X2)
| ~ product(j,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f25,f33]) ).
fof(f55,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ product(c,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f25,f30]) ).
fof(f60,plain,
! [X0,X1,X2] :
( product(k,X0,X2)
| ~ product(j,X1,X2)
| ~ product(inverse(h),X0,X1) ),
inference(resolution,[status(thm)],[f27,f34]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( product(multiply(X3,X0),X1,X4)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f21,f27]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X2,X4)
| ~ product(multiply(X3,X0),X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f21,f25]) ).
fof(f69,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f21,f23]) ).
fof(f70,plain,
! [X0] : product(multiply(X0,X0),X0,identity),
inference(resolution,[status(thm)],[f21,f29]) ).
fof(f71,plain,
! [X0] : product(X0,multiply(X0,X0),identity),
inference(resolution,[status(thm)],[f21,f28]) ).
fof(f73,plain,
inverse(identity) = identity,
inference(resolution,[status(thm)],[f41,f20]) ).
fof(f82,plain,
! [X0] : X0 = multiply(X0,identity),
inference(resolution,[status(thm)],[f48,f21]) ).
fof(f114,plain,
d = multiply(c,inverse(a)),
inference(resolution,[status(thm)],[f44,f21]) ).
fof(f116,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f46,f21]) ).
fof(f141,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(resolution,[status(thm)],[f69,f71]) ).
fof(f162,plain,
! [X0,X1] :
( product(inverse(inverse(X0)),identity,X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f49,f19]) ).
fof(f172,plain,
! [X0,X1,X2] :
( product(inverse(X2),multiply(X2,X0),X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f49,f21]) ).
fof(f233,plain,
! [X0] :
( product(d,identity,X0)
| ~ product(h,b,X0) ),
inference(resolution,[status(thm)],[f52,f19]) ).
fof(f238,plain,
! [X0] :
( product(c,identity,X0)
| ~ product(d,a,X0) ),
inference(resolution,[status(thm)],[f53,f19]) ).
fof(f246,plain,
! [X0,X1] :
( product(h,multiply(b,X0),X1)
| ~ product(j,X0,X1) ),
inference(resolution,[status(thm)],[f54,f21]) ).
fof(f254,plain,
product(d,identity,j),
inference(resolution,[status(thm)],[f233,f33]) ).
fof(f260,plain,
! [X0,X1] :
( product(a,multiply(b,X0),X1)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f55,f21]) ).
fof(f262,plain,
d = j,
inference(resolution,[status(thm)],[f254,f48]) ).
fof(f346,plain,
product(c,identity,multiply(d,a)),
inference(resolution,[status(thm)],[f238,f21]) ).
fof(f348,plain,
c = multiply(d,a),
inference(resolution,[status(thm)],[f346,f48]) ).
fof(f358,plain,
product(d,a,c),
inference(paramodulation,[status(thm)],[f348,f21]) ).
fof(f359,plain,
! [X0,X1,X2] :
( product(k,X0,X2)
| ~ product(d,X1,X2)
| ~ product(inverse(h),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f262,f60]) ).
fof(f548,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0),
inference(resolution,[status(thm)],[f162,f17]) ).
fof(f565,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[f548,f48]) ).
fof(f619,plain,
! [X0,X1,X2] :
( product(multiply(X0,multiply(X2,X2)),X2,X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f67,f70]) ).
fof(f627,plain,
! [X0,X1] :
( product(multiply(X0,a),b,X1)
| ~ product(X0,c,X1) ),
inference(resolution,[status(thm)],[f67,f30]) ).
fof(f631,plain,
! [X0,X1,X2,X3] :
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f67,f21]) ).
fof(f642,plain,
! [X0,X1] :
( product(X0,c,X1)
| ~ product(multiply(X0,a),b,X1) ),
inference(resolution,[status(thm)],[f68,f30]) ).
fof(f775,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f172,f17]) ).
fof(f802,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[f775,f69]) ).
fof(f805,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ product(inverse(X0),multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f775,f23]) ).
fof(f814,plain,
product(inverse(d),c,a),
inference(paramodulation,[status(thm)],[f348,f775]) ).
fof(f900,plain,
multiply(inverse(d),c) = a,
inference(resolution,[status(thm)],[f814,f69]) ).
fof(f937,plain,
! [X0] : multiply(inverse(X0),identity) = multiply(X0,X0),
inference(paramodulation,[status(thm)],[f141,f802]) ).
fof(f952,plain,
! [X0] : inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[status(thm)],[f82,f937]) ).
fof(f991,plain,
! [X0] : product(X0,X0,inverse(X0)),
inference(paramodulation,[status(thm)],[f952,f21]) ).
fof(f1016,plain,
! [X0,X1,X2] :
( product(X0,inverse(X1),X2)
| ~ product(multiply(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f991,f68]) ).
fof(f1465,plain,
! [X0,X1] : product(X0,inverse(X1),multiply(multiply(X0,X1),X1)),
inference(resolution,[status(thm)],[f1016,f21]) ).
fof(f1541,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = multiply(multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f1465,f69]) ).
fof(f1737,plain,
multiply(c,inverse(inverse(a))) = multiply(d,inverse(a)),
inference(paramodulation,[status(thm)],[f114,f1541]) ).
fof(f1762,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,inverse(X1))) = X1,
inference(paramodulation,[status(thm)],[f1541,f802]) ).
fof(f1763,plain,
! [X0,X1] : product(inverse(multiply(X0,X1)),multiply(X0,inverse(X1)),X1),
inference(paramodulation,[status(thm)],[f1541,f775]) ).
fof(f1766,plain,
! [X0,X1] : product(multiply(X0,X1),X1,multiply(X0,inverse(X1))),
inference(paramodulation,[status(thm)],[f1541,f21]) ).
fof(f1767,plain,
multiply(c,a) = multiply(d,inverse(a)),
inference(forward_demodulation,[status(thm)],[f565,f1737]) ).
fof(f2119,plain,
! [X0,X1] :
( product(h,multiply(b,X0),X1)
| ~ product(d,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f262,f246]) ).
fof(f2123,plain,
product(h,multiply(b,a),c),
inference(resolution,[status(thm)],[f2119,f358]) ).
fof(f2144,plain,
multiply(h,multiply(b,a)) = c,
inference(resolution,[status(thm)],[f2123,f69]) ).
fof(f2153,plain,
multiply(inverse(h),c) = multiply(b,a),
inference(paramodulation,[status(thm)],[f2144,f802]) ).
fof(f2237,plain,
! [X0] : product(a,multiply(b,X0),multiply(c,X0)),
inference(resolution,[status(thm)],[f260,f21]) ).
fof(f2620,plain,
! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(resolution,[status(thm)],[f2237,f69]) ).
fof(f2883,plain,
! [X0] : multiply(inverse(a),multiply(c,X0)) = multiply(b,X0),
inference(paramodulation,[status(thm)],[f2620,f802]) ).
fof(f4116,plain,
! [X0,X1,X2] :
( product(multiply(X0,inverse(X2)),X2,X1)
| ~ product(X0,identity,X1) ),
inference(forward_demodulation,[status(thm)],[f952,f619]) ).
fof(f4117,plain,
! [X0,X1] : product(multiply(multiply(X0,identity),inverse(X1)),X1,multiply(X0,inverse(identity))),
inference(resolution,[status(thm)],[f4116,f1766]) ).
fof(f4123,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,multiply(X0,inverse(identity))),
inference(forward_demodulation,[status(thm)],[f82,f4117]) ).
fof(f4124,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,multiply(X0,identity)),
inference(forward_demodulation,[status(thm)],[f73,f4123]) ).
fof(f4125,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,X0),
inference(forward_demodulation,[status(thm)],[f82,f4124]) ).
fof(f4149,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(resolution,[status(thm)],[f4125,f69]) ).
fof(f4215,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f565,f4149]) ).
fof(f4223,plain,
! [X0,X1] : multiply(inverse(multiply(multiply(X0,inverse(inverse(X1))),X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f4149,f1762]) ).
fof(f4255,plain,
! [X0,X1] : multiply(inverse(multiply(multiply(X0,X1),X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f565,f4223]) ).
fof(f4256,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f1541,f4255]) ).
fof(f4397,plain,
multiply(a,inverse(c)) = inverse(d),
inference(paramodulation,[status(thm)],[f900,f4215]) ).
fof(f4404,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f802,f4215]) ).
fof(f4612,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f4256,f4215]) ).
fof(f4690,plain,
product(multiply(c,a),b,inverse(c)),
inference(resolution,[status(thm)],[f627,f991]) ).
fof(f5207,plain,
! [X0,X1] : product(inverse(inverse(X0)),multiply(X1,inverse(inverse(multiply(X0,X1)))),inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f4404,f1763]) ).
fof(f5265,plain,
! [X0,X1] : product(X0,multiply(X1,inverse(inverse(multiply(X0,X1)))),inverse(multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f565,f5207]) ).
fof(f5266,plain,
! [X0,X1] : product(X0,multiply(X1,multiply(X0,X1)),inverse(multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f565,f5265]) ).
fof(f5581,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f631,f21]) ).
fof(f6324,plain,
! [X0] : product(X0,c,multiply(multiply(X0,a),b)),
inference(resolution,[status(thm)],[f642,f21]) ).
fof(f6442,plain,
multiply(multiply(c,a),b) = inverse(c),
inference(resolution,[status(thm)],[f4690,f69]) ).
fof(f7746,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[f5581,f69]) ).
fof(f7809,plain,
! [X0,X1] : product(inverse(X0),X1,multiply(X0,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f952,f5581]) ).
fof(f7955,plain,
! [X0,X1] : X0 = multiply(X1,multiply(X1,multiply(X1,X0))),
inference(resolution,[status(thm)],[f7809,f805]) ).
fof(f8274,plain,
! [X0,X1] : product(X0,multiply(X0,multiply(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f7955,f21]) ).
fof(f8415,plain,
! [X0,X1] : product(X0,multiply(X0,inverse(X1)),inverse(multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f4404,f8274]) ).
fof(f9411,plain,
! [X0] :
( product(k,c,X0)
| ~ product(d,multiply(multiply(inverse(h),a),b),X0) ),
inference(resolution,[status(thm)],[f6324,f359]) ).
fof(f9555,plain,
multiply(b,inverse(inverse(c))) = inverse(multiply(c,a)),
inference(paramodulation,[status(thm)],[f6442,f4404]) ).
fof(f9580,plain,
multiply(b,c) = inverse(multiply(c,a)),
inference(forward_demodulation,[status(thm)],[f565,f9555]) ).
fof(f16610,plain,
product(a,inverse(d),inverse(multiply(c,a))),
inference(paramodulation,[status(thm)],[f4397,f8415]) ).
fof(f16764,plain,
product(a,inverse(d),multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f9580,f16610]) ).
fof(f16922,plain,
multiply(a,inverse(d)) = multiply(b,c),
inference(resolution,[status(thm)],[f16764,f69]) ).
fof(f26126,plain,
product(d,multiply(inverse(a),multiply(c,a)),inverse(multiply(d,inverse(a)))),
inference(paramodulation,[status(thm)],[f1767,f5266]) ).
fof(f26494,plain,
product(d,multiply(b,a),inverse(multiply(d,inverse(a)))),
inference(forward_demodulation,[status(thm)],[f2883,f26126]) ).
fof(f26495,plain,
product(d,multiply(b,a),multiply(a,inverse(d))),
inference(forward_demodulation,[status(thm)],[f4612,f26494]) ).
fof(f26496,plain,
product(d,multiply(b,a),multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f16922,f26495]) ).
fof(f32191,plain,
! [X0] :
( product(k,c,X0)
| ~ product(d,multiply(inverse(h),multiply(a,b)),X0) ),
inference(forward_demodulation,[status(thm)],[f7746,f9411]) ).
fof(f32192,plain,
! [X0] :
( product(k,c,X0)
| ~ product(d,multiply(inverse(h),c),X0) ),
inference(forward_demodulation,[status(thm)],[f116,f32191]) ).
fof(f32193,plain,
! [X0] :
( product(k,c,X0)
| ~ product(d,multiply(b,a),X0) ),
inference(forward_demodulation,[status(thm)],[f2153,f32192]) ).
fof(f54098,plain,
product(k,c,multiply(b,c)),
inference(resolution,[status(thm)],[f26496,f32193]) ).
fof(f54141,plain,
multiply(k,c) = multiply(b,c),
inference(resolution,[status(thm)],[f54098,f69]) ).
fof(f54273,plain,
multiply(c,inverse(multiply(k,c))) = inverse(b),
inference(paramodulation,[status(thm)],[f54141,f4404]) ).
fof(f54331,plain,
inverse(k) = inverse(b),
inference(forward_demodulation,[status(thm)],[f4404,f54273]) ).
fof(f54433,plain,
~ product(k,inverse(k),identity),
inference(backward_demodulation,[status(thm)],[f54331,f35]) ).
fof(f54524,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f54433,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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 : Sun Sep 20 19:58:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 57.34/7.66 % Refutation found
% 57.34/7.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 57.34/7.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 57.34/7.72 % Elapsed time: 7.337126 seconds
% 57.34/7.72 % CPU time: 57.906408 seconds
% 57.34/7.72 % Total memory used: 227.080 MB
% 57.34/7.72 % Net memory used: 183.861 MB
%------------------------------------------------------------------------------