TSTP Solution File: GRP002-10 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:18:43 EDT 2024
% Result : Unsatisfiable 19.92s 2.86s
% Output : CNFRefutation 20.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 17
% Syntax : Number of formulae : 168 ( 168 unt; 0 def)
% Number of atoms : 168 ( 167 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 261 ( 261 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(identity,X,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,identity,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : product(inverse(X),X,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : product(X,inverse(X),identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,W,Z] : ifeq2(product(X,Y,W),true,ifeq2(product(X,Y,Z),true,Z,W),W) = W,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,Z,W,Y,V,X] : ifeq(product(U,Z,W),true,ifeq(product(Y,Z,V),true,ifeq(product(X,Y,U),true,product(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,Z,V,X,W,U] : ifeq(product(Y,Z,V),true,ifeq(product(X,V,W),true,ifeq(product(X,Y,U),true,product(U,Z,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [X,Y] : ifeq(product(X,X,Y),true,product(X,Y,identity),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
product(a,b,c) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
product(c,inverse(a),d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
product(d,inverse(b),h) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
product(h,b,j) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
product(j,inverse(h),k) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
product(k,inverse(b),identity) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [X0] : product(identity,X0,X0) = true,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0] : product(X0,identity,X0) = true,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0] : product(inverse(X0),X0,identity) = true,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
! [X0] : product(X0,inverse(X0),identity) = true,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f28,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f29,plain,
! [X0,X1] : ifeq(product(X0,X0,X1),true,product(X0,X1,identity),true) = true,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f31,plain,
product(a,b,c) = true,
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f32,plain,
product(c,inverse(a),d) = true,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f33,plain,
product(d,inverse(b),h) = true,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f34,plain,
product(h,b,j) = true,
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f35,plain,
product(j,inverse(h),k) = true,
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f36,plain,
product(k,inverse(b),identity) != true,
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
! [X0] : ifeq2(true,true,ifeq2(product(h,b,X0),true,X0,j),j) = j,
inference(paramodulation,[status(thm)],[f34,f26]) ).
fof(f42,plain,
! [X0] : ifeq2(product(h,b,X0),true,X0,j) = j,
inference(forward_demodulation,[status(thm)],[f19,f41]) ).
fof(f51,plain,
! [X0,X1] : ifeq2(true,true,ifeq2(product(X0,identity,X1),true,X1,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f22,f26]) ).
fof(f52,plain,
! [X0,X1] : ifeq2(product(X0,identity,X1),true,X1,X0) = X0,
inference(forward_demodulation,[status(thm)],[f19,f51]) ).
fof(f53,plain,
! [X0,X1,X2] : ifeq2(true,true,ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),multiply(X0,X1)) = multiply(X0,X1),
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f54,plain,
! [X0,X1,X2] : ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f19,f53]) ).
fof(f69,plain,
! [X0,X1] : ifeq2(product(X0,identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f22,f26]) ).
fof(f70,plain,
! [X0,X1] : ifeq2(product(X0,identity,X1),true,X0,X1) = X1,
inference(forward_demodulation,[status(thm)],[f19,f69]) ).
fof(f71,plain,
! [X0,X1,X2] : ifeq2(product(X0,X1,X2),true,ifeq2(true,true,multiply(X0,X1),X2),X2) = X2,
inference(paramodulation,[status(thm)],[f25,f26]) ).
fof(f72,plain,
! [X0,X1,X2] : ifeq2(product(X0,X1,X2),true,multiply(X0,X1),X2) = X2,
inference(forward_demodulation,[status(thm)],[f19,f71]) ).
fof(f87,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,inverse(h),X1),true,ifeq(product(X2,X0,j),true,product(X2,X1,k),true),true),true) = true,
inference(paramodulation,[status(thm)],[f35,f27]) ).
fof(f88,plain,
! [X0,X1,X2] : ifeq(product(X0,inverse(h),X1),true,ifeq(product(X2,X0,j),true,product(X2,X1,k),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f87]) ).
fof(f89,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,inverse(b),X1),true,ifeq(product(X2,X0,d),true,product(X2,X1,h),true),true),true) = true,
inference(paramodulation,[status(thm)],[f33,f27]) ).
fof(f90,plain,
! [X0,X1,X2] : ifeq(product(X0,inverse(b),X1),true,ifeq(product(X2,X0,d),true,product(X2,X1,h),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f89]) ).
fof(f91,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,inverse(a),X1),true,ifeq(product(X2,X0,c),true,product(X2,X1,d),true),true),true) = true,
inference(paramodulation,[status(thm)],[f32,f27]) ).
fof(f92,plain,
! [X0,X1,X2] : ifeq(product(X0,inverse(a),X1),true,ifeq(product(X2,X0,c),true,product(X2,X1,d),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f91]) ).
fof(f95,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,b,X1),true,ifeq(product(X2,X0,a),true,product(X2,X1,c),true),true),true) = true,
inference(paramodulation,[status(thm)],[f31,f27]) ).
fof(f96,plain,
! [X0,X1,X2] : ifeq(product(X0,b,X1),true,ifeq(product(X2,X0,a),true,product(X2,X1,c),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f95]) ).
fof(f99,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f100,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f99]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4] : ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X3,X2,multiply(X4,X1)),true),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X3,X2,multiply(X4,X1)),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f105]) ).
fof(f161,plain,
! [X0] : ifeq2(true,true,multiply(X0,identity),X0) = X0,
inference(paramodulation,[status(thm)],[f25,f52]) ).
fof(f162,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f19,f161]) ).
fof(f193,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(product(X0,identity,X1),true,ifeq(product(X0,inverse(X2),X3),true,product(X3,X2,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f23,f28]) ).
fof(f194,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,identity,X1),true,ifeq(product(X0,inverse(X2),X3),true,product(X3,X2,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f193]) ).
fof(f274,plain,
! [X0] : ifeq(true,true,product(X0,multiply(X0,X0),identity),true) = true,
inference(paramodulation,[status(thm)],[f25,f29]) ).
fof(f275,plain,
! [X0] : product(X0,multiply(X0,X0),identity) = true,
inference(forward_demodulation,[status(thm)],[f20,f274]) ).
fof(f335,plain,
! [X0] : ifeq2(true,true,multiply(X0,multiply(X0,X0)),identity) = identity,
inference(paramodulation,[status(thm)],[f275,f72]) ).
fof(f336,plain,
! [X0] : multiply(X0,multiply(X0,X0)) = identity,
inference(forward_demodulation,[status(thm)],[f19,f335]) ).
fof(f547,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,X1,j),true,product(X0,multiply(X1,inverse(h)),k),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f88]) ).
fof(f548,plain,
! [X0,X1] : ifeq(product(X0,X1,j),true,product(X0,multiply(X1,inverse(h)),k),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f547]) ).
fof(f583,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,X1,d),true,product(X0,multiply(X1,inverse(b)),h),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f90]) ).
fof(f584,plain,
! [X0,X1] : ifeq(product(X0,X1,d),true,product(X0,multiply(X1,inverse(b)),h),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f583]) ).
fof(f620,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,X1,c),true,product(X0,multiply(X1,inverse(a)),d),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f92]) ).
fof(f621,plain,
! [X0,X1] : ifeq(product(X0,X1,c),true,product(X0,multiply(X1,inverse(a)),d),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f620]) ).
fof(f706,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,X1,a),true,product(X0,multiply(X1,b),c),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f96]) ).
fof(f707,plain,
! [X0,X1] : ifeq(product(X0,X1,a),true,product(X0,multiply(X1,b),c),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f706]) ).
fof(f849,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,ifeq(true,true,product(inverse(X0),X2,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f23,f100]) ).
fof(f850,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,product(inverse(X0),X2,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f849]) ).
fof(f855,plain,
! [X0,X1,X2] : ifeq(product(inverse(X0),X1,X2),true,ifeq(true,true,product(X0,X2,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f24,f100]) ).
fof(f856,plain,
! [X0,X1,X2] : ifeq(product(inverse(X0),X1,X2),true,product(X0,X2,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f855]) ).
fof(f905,plain,
! [X0] : ifeq(true,true,product(inverse(inverse(X0)),identity,X0),true) = true,
inference(paramodulation,[status(thm)],[f23,f850]) ).
fof(f906,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0) = true,
inference(forward_demodulation,[status(thm)],[f20,f905]) ).
fof(f916,plain,
! [X0,X1] : ifeq(true,true,product(inverse(X0),multiply(X0,X1),X1),true) = true,
inference(paramodulation,[status(thm)],[f25,f850]) ).
fof(f917,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1) = true,
inference(forward_demodulation,[status(thm)],[f20,f916]) ).
fof(f1075,plain,
! [X0] : ifeq2(true,true,inverse(inverse(X0)),X0) = X0,
inference(paramodulation,[status(thm)],[f906,f70]) ).
fof(f1076,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f19,f1075]) ).
fof(f1298,plain,
! [X0,X1] : ifeq2(true,true,X0,multiply(inverse(X1),multiply(X1,X0))) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f917,f54]) ).
fof(f1299,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f19,f1298]) ).
fof(f1320,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f1076,f1299]) ).
fof(f1339,plain,
! [X0] : multiply(X0,X0) = multiply(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f336,f1299]) ).
fof(f1340,plain,
! [X0] : multiply(X0,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f162,f1339]) ).
fof(f1359,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,a,X1),true,product(X0,c,multiply(X1,b)),true),true) = true,
inference(paramodulation,[status(thm)],[f31,f106]) ).
fof(f1360,plain,
! [X0,X1] : ifeq(product(X0,a,X1),true,product(X0,c,multiply(X1,b)),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f1359]) ).
fof(f1378,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(product(X0,X1,X2),true,product(X0,multiply(X1,X3),multiply(X2,X3)),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f106]) ).
fof(f1379,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,product(X0,multiply(X1,X3),multiply(X2,X3)),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f1378]) ).
fof(f1483,plain,
! [X0] : product(X0,X0,inverse(X0)) = true,
inference(paramodulation,[status(thm)],[f1340,f25]) ).
fof(f4870,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,inverse(X1),X2),true,product(X2,X1,X0),true),true) = true,
inference(paramodulation,[status(thm)],[f22,f194]) ).
fof(f4871,plain,
! [X0,X1,X2] : ifeq(product(X0,inverse(X1),X2),true,product(X2,X1,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f4870]) ).
fof(f5550,plain,
ifeq(true,true,product(h,b,d),true) = true,
inference(paramodulation,[status(thm)],[f33,f4871]) ).
fof(f5551,plain,
product(h,b,d) = true,
inference(forward_demodulation,[status(thm)],[f20,f5550]) ).
fof(f5552,plain,
ifeq(true,true,product(d,a,c),true) = true,
inference(paramodulation,[status(thm)],[f32,f4871]) ).
fof(f5553,plain,
product(d,a,c) = true,
inference(forward_demodulation,[status(thm)],[f20,f5552]) ).
fof(f5566,plain,
! [X0,X1] : ifeq(true,true,product(multiply(X0,inverse(X1)),X1,X0),true) = true,
inference(paramodulation,[status(thm)],[f25,f4871]) ).
fof(f5567,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,X0) = true,
inference(forward_demodulation,[status(thm)],[f20,f5566]) ).
fof(f5741,plain,
ifeq2(true,true,d,j) = j,
inference(paramodulation,[status(thm)],[f5551,f42]) ).
fof(f5742,plain,
d = j,
inference(forward_demodulation,[status(thm)],[f19,f5741]) ).
fof(f6176,plain,
ifeq(true,true,product(inverse(d),c,a),true) = true,
inference(paramodulation,[status(thm)],[f5553,f850]) ).
fof(f6177,plain,
product(inverse(d),c,a) = true,
inference(forward_demodulation,[status(thm)],[f20,f6176]) ).
fof(f6711,plain,
! [X0,X1] : product(multiply(X0,X1),inverse(X1),X0) = true,
inference(paramodulation,[status(thm)],[f1076,f5567]) ).
fof(f6976,plain,
! [X0,X1] : ifeq2(true,true,X0,multiply(multiply(X0,inverse(X1)),X1)) = multiply(multiply(X0,inverse(X1)),X1),
inference(paramodulation,[status(thm)],[f5567,f54]) ).
fof(f6977,plain,
! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(forward_demodulation,[status(thm)],[f19,f6976]) ).
fof(f7014,plain,
! [X0,X1] : X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(paramodulation,[status(thm)],[f1076,f6977]) ).
fof(f7165,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f1299,f7014]) ).
fof(f7186,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f7014,f1299]) ).
fof(f8285,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f7014,f7165]) ).
fof(f8441,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f1320,f7186]) ).
fof(f15797,plain,
! [X0,X1] : ifeq(product(X0,X1,d),true,product(X0,multiply(X1,inverse(h)),k),true) = true,
inference(forward_demodulation,[status(thm)],[f5742,f548]) ).
fof(f15806,plain,
ifeq(true,true,product(c,multiply(inverse(a),inverse(h)),k),true) = true,
inference(paramodulation,[status(thm)],[f32,f15797]) ).
fof(f15807,plain,
product(c,multiply(inverse(a),inverse(h)),k) = true,
inference(forward_demodulation,[status(thm)],[f20,f15806]) ).
fof(f15808,plain,
product(c,inverse(multiply(h,a)),k) = true,
inference(forward_demodulation,[status(thm)],[f8285,f15807]) ).
fof(f15982,plain,
ifeq2(true,true,k,multiply(c,inverse(multiply(h,a)))) = multiply(c,inverse(multiply(h,a))),
inference(paramodulation,[status(thm)],[f15808,f54]) ).
fof(f15983,plain,
k = multiply(c,inverse(multiply(h,a))),
inference(forward_demodulation,[status(thm)],[f19,f15982]) ).
fof(f17992,plain,
! [X0] : ifeq(true,true,product(multiply(d,X0),multiply(inverse(X0),inverse(b)),h),true) = true,
inference(paramodulation,[status(thm)],[f6711,f584]) ).
fof(f17993,plain,
! [X0] : product(multiply(d,X0),multiply(inverse(X0),inverse(b)),h) = true,
inference(forward_demodulation,[status(thm)],[f20,f17992]) ).
fof(f17994,plain,
! [X0] : product(multiply(d,X0),inverse(multiply(b,X0)),h) = true,
inference(forward_demodulation,[status(thm)],[f8285,f17993]) ).
fof(f19979,plain,
! [X0] : ifeq(true,true,product(multiply(c,X0),multiply(inverse(X0),inverse(a)),d),true) = true,
inference(paramodulation,[status(thm)],[f6711,f621]) ).
fof(f19980,plain,
! [X0] : product(multiply(c,X0),multiply(inverse(X0),inverse(a)),d) = true,
inference(forward_demodulation,[status(thm)],[f20,f19979]) ).
fof(f19981,plain,
! [X0] : product(multiply(c,X0),inverse(multiply(a,X0)),d) = true,
inference(forward_demodulation,[status(thm)],[f8285,f19980]) ).
fof(f23295,plain,
ifeq(true,true,product(inverse(d),multiply(c,b),c),true) = true,
inference(paramodulation,[status(thm)],[f6177,f707]) ).
fof(f23296,plain,
product(inverse(d),multiply(c,b),c) = true,
inference(forward_demodulation,[status(thm)],[f20,f23295]) ).
fof(f23968,plain,
ifeq(true,true,product(d,c,multiply(c,b)),true) = true,
inference(paramodulation,[status(thm)],[f23296,f856]) ).
fof(f23969,plain,
product(d,c,multiply(c,b)) = true,
inference(forward_demodulation,[status(thm)],[f20,f23968]) ).
fof(f24259,plain,
ifeq2(true,true,multiply(c,b),multiply(d,c)) = multiply(d,c),
inference(paramodulation,[status(thm)],[f23969,f54]) ).
fof(f24260,plain,
multiply(c,b) = multiply(d,c),
inference(forward_demodulation,[status(thm)],[f19,f24259]) ).
fof(f27639,plain,
! [X0] : ifeq(true,true,product(h,multiply(b,X0),multiply(d,X0)),true) = true,
inference(paramodulation,[status(thm)],[f17994,f4871]) ).
fof(f27640,plain,
! [X0] : product(h,multiply(b,X0),multiply(d,X0)) = true,
inference(forward_demodulation,[status(thm)],[f20,f27639]) ).
fof(f28195,plain,
! [X0] : ifeq2(true,true,multiply(d,X0),multiply(h,multiply(b,X0))) = multiply(h,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f27640,f54]) ).
fof(f28196,plain,
! [X0] : multiply(d,X0) = multiply(h,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f19,f28195]) ).
fof(f37983,plain,
! [X0] : ifeq2(true,true,d,multiply(multiply(c,X0),inverse(multiply(a,X0)))) = multiply(multiply(c,X0),inverse(multiply(a,X0))),
inference(paramodulation,[status(thm)],[f19981,f54]) ).
fof(f37984,plain,
! [X0] : d = multiply(multiply(c,X0),inverse(multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f19,f37983]) ).
fof(f38637,plain,
d = multiply(inverse(c),inverse(multiply(a,c))),
inference(paramodulation,[status(thm)],[f1340,f37984]) ).
fof(f38638,plain,
d = inverse(multiply(multiply(a,c),c)),
inference(forward_demodulation,[status(thm)],[f8285,f38637]) ).
fof(f38721,plain,
inverse(multiply(a,c)) = multiply(c,d),
inference(paramodulation,[status(thm)],[f38638,f7165]) ).
fof(f43798,plain,
ifeq(true,true,product(a,c,multiply(inverse(a),b)),true) = true,
inference(paramodulation,[status(thm)],[f1483,f1360]) ).
fof(f43799,plain,
product(a,c,multiply(inverse(a),b)) = true,
inference(forward_demodulation,[status(thm)],[f20,f43798]) ).
fof(f45134,plain,
ifeq2(true,true,multiply(inverse(a),b),multiply(a,c)) = multiply(a,c),
inference(paramodulation,[status(thm)],[f43799,f54]) ).
fof(f45135,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(forward_demodulation,[status(thm)],[f19,f45134]) ).
fof(f45211,plain,
inverse(inverse(a)) = multiply(b,inverse(multiply(a,c))),
inference(paramodulation,[status(thm)],[f45135,f7165]) ).
fof(f45212,plain,
a = multiply(b,inverse(multiply(a,c))),
inference(forward_demodulation,[status(thm)],[f1076,f45211]) ).
fof(f45213,plain,
a = multiply(b,multiply(c,d)),
inference(forward_demodulation,[status(thm)],[f38721,f45212]) ).
fof(f45503,plain,
! [X0,X1] : ifeq(true,true,product(X0,multiply(X0,X1),multiply(inverse(X0),X1)),true) = true,
inference(paramodulation,[status(thm)],[f1483,f1379]) ).
fof(f45504,plain,
! [X0,X1] : product(X0,multiply(X0,X1),multiply(inverse(X0),X1)) = true,
inference(forward_demodulation,[status(thm)],[f20,f45503]) ).
fof(f45505,plain,
! [X0,X1,X2] : ifeq(true,true,product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),true) = true,
inference(paramodulation,[status(thm)],[f25,f1379]) ).
fof(f45506,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)) = true,
inference(forward_demodulation,[status(thm)],[f20,f45505]) ).
fof(f45851,plain,
multiply(d,multiply(c,d)) = multiply(h,a),
inference(paramodulation,[status(thm)],[f45213,f28196]) ).
fof(f47138,plain,
! [X0,X1] : ifeq2(true,true,multiply(inverse(X0),X1),multiply(X0,multiply(X0,X1))) = multiply(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f45504,f54]) ).
fof(f47139,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f47138]) ).
fof(f48507,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(X1)) = multiply(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f7014,f47139]) ).
fof(f48508,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,X0))) = multiply(multiply(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f8285,f48507]) ).
fof(f59414,plain,
! [X0,X1,X2] : ifeq2(true,true,multiply(multiply(X0,X1),X2),multiply(X0,multiply(X1,X2))) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f45506,f54]) ).
fof(f59415,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f19,f59414]) ).
fof(f61755,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,X0))) = multiply(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f59415,f48508]) ).
fof(f61957,plain,
inverse(multiply(c,multiply(c,b))) = multiply(d,multiply(c,d)),
inference(paramodulation,[status(thm)],[f24260,f61755]) ).
fof(f61958,plain,
inverse(multiply(inverse(c),b)) = multiply(d,multiply(c,d)),
inference(forward_demodulation,[status(thm)],[f47139,f61957]) ).
fof(f61959,plain,
multiply(inverse(b),c) = multiply(d,multiply(c,d)),
inference(forward_demodulation,[status(thm)],[f8441,f61958]) ).
fof(f61960,plain,
multiply(inverse(b),c) = multiply(h,a),
inference(forward_demodulation,[status(thm)],[f45851,f61959]) ).
fof(f62762,plain,
inverse(inverse(b)) = multiply(c,inverse(multiply(h,a))),
inference(paramodulation,[status(thm)],[f61960,f7165]) ).
fof(f62763,plain,
b = multiply(c,inverse(multiply(h,a))),
inference(forward_demodulation,[status(thm)],[f1076,f62762]) ).
fof(f62764,plain,
b = k,
inference(forward_demodulation,[status(thm)],[f15983,f62763]) ).
fof(f62913,plain,
product(b,inverse(b),identity) != true,
inference(backward_demodulation,[status(thm)],[f62764,f36]) ).
fof(f62914,plain,
true != true,
inference(forward_demodulation,[status(thm)],[f24,f62913]) ).
fof(f62915,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f62914]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n016.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 30 00:59:55 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.6.0
% 19.92/2.86 % Refutation found
% 19.92/2.86 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 19.92/2.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.27/2.99 % Elapsed time: 2.665553 seconds
% 21.27/2.99 % CPU time: 20.750844 seconds
% 21.27/2.99 % Total memory used: 390.546 MB
% 21.27/2.99 % Net memory used: 379.606 MB
%------------------------------------------------------------------------------