TSTP Solution File: GRP002-10 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% 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 : n026.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 : Wed May 31 12:09:38 EDT 2023
% Result : Unsatisfiable 13.22s 2.02s
% Output : CNFRefutation 13.22s
% 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(f4863,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(f4864,plain,
! [X0,X1,X2] : ifeq(product(X0,inverse(X1),X2),true,product(X2,X1,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f4863]) ).
fof(f5543,plain,
ifeq(true,true,product(h,b,d),true) = true,
inference(paramodulation,[status(thm)],[f33,f4864]) ).
fof(f5544,plain,
product(h,b,d) = true,
inference(forward_demodulation,[status(thm)],[f20,f5543]) ).
fof(f5545,plain,
ifeq(true,true,product(d,a,c),true) = true,
inference(paramodulation,[status(thm)],[f32,f4864]) ).
fof(f5546,plain,
product(d,a,c) = true,
inference(forward_demodulation,[status(thm)],[f20,f5545]) ).
fof(f5559,plain,
! [X0,X1] : ifeq(true,true,product(multiply(X0,inverse(X1)),X1,X0),true) = true,
inference(paramodulation,[status(thm)],[f25,f4864]) ).
fof(f5560,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,X0) = true,
inference(forward_demodulation,[status(thm)],[f20,f5559]) ).
fof(f5734,plain,
ifeq2(true,true,d,j) = j,
inference(paramodulation,[status(thm)],[f5544,f42]) ).
fof(f5735,plain,
d = j,
inference(forward_demodulation,[status(thm)],[f19,f5734]) ).
fof(f6169,plain,
ifeq(true,true,product(inverse(d),c,a),true) = true,
inference(paramodulation,[status(thm)],[f5546,f850]) ).
fof(f6170,plain,
product(inverse(d),c,a) = true,
inference(forward_demodulation,[status(thm)],[f20,f6169]) ).
fof(f6703,plain,
! [X0,X1] : product(multiply(X0,X1),inverse(X1),X0) = true,
inference(paramodulation,[status(thm)],[f1076,f5560]) ).
fof(f6968,plain,
! [X0,X1] : ifeq2(true,true,X0,multiply(multiply(X0,inverse(X1)),X1)) = multiply(multiply(X0,inverse(X1)),X1),
inference(paramodulation,[status(thm)],[f5560,f54]) ).
fof(f6969,plain,
! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(forward_demodulation,[status(thm)],[f19,f6968]) ).
fof(f7006,plain,
! [X0,X1] : X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(paramodulation,[status(thm)],[f1076,f6969]) ).
fof(f7041,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f1299,f7006]) ).
fof(f7062,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f7006,f1299]) ).
fof(f8276,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f7006,f7041]) ).
fof(f8393,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f1320,f7062]) ).
fof(f15956,plain,
! [X0,X1] : ifeq(product(X0,X1,d),true,product(X0,multiply(X1,inverse(h)),k),true) = true,
inference(forward_demodulation,[status(thm)],[f5735,f548]) ).
fof(f15965,plain,
ifeq(true,true,product(c,multiply(inverse(a),inverse(h)),k),true) = true,
inference(paramodulation,[status(thm)],[f32,f15956]) ).
fof(f15966,plain,
product(c,multiply(inverse(a),inverse(h)),k) = true,
inference(forward_demodulation,[status(thm)],[f20,f15965]) ).
fof(f15967,plain,
product(c,inverse(multiply(h,a)),k) = true,
inference(forward_demodulation,[status(thm)],[f8276,f15966]) ).
fof(f16145,plain,
ifeq2(true,true,k,multiply(c,inverse(multiply(h,a)))) = multiply(c,inverse(multiply(h,a))),
inference(paramodulation,[status(thm)],[f15967,f54]) ).
fof(f16146,plain,
k = multiply(c,inverse(multiply(h,a))),
inference(forward_demodulation,[status(thm)],[f19,f16145]) ).
fof(f18127,plain,
! [X0] : ifeq(true,true,product(multiply(d,X0),multiply(inverse(X0),inverse(b)),h),true) = true,
inference(paramodulation,[status(thm)],[f6703,f584]) ).
fof(f18128,plain,
! [X0] : product(multiply(d,X0),multiply(inverse(X0),inverse(b)),h) = true,
inference(forward_demodulation,[status(thm)],[f20,f18127]) ).
fof(f18129,plain,
! [X0] : product(multiply(d,X0),inverse(multiply(b,X0)),h) = true,
inference(forward_demodulation,[status(thm)],[f8276,f18128]) ).
fof(f20180,plain,
! [X0] : ifeq(true,true,product(multiply(c,X0),multiply(inverse(X0),inverse(a)),d),true) = true,
inference(paramodulation,[status(thm)],[f6703,f621]) ).
fof(f20181,plain,
! [X0] : product(multiply(c,X0),multiply(inverse(X0),inverse(a)),d) = true,
inference(forward_demodulation,[status(thm)],[f20,f20180]) ).
fof(f20182,plain,
! [X0] : product(multiply(c,X0),inverse(multiply(a,X0)),d) = true,
inference(forward_demodulation,[status(thm)],[f8276,f20181]) ).
fof(f23520,plain,
ifeq(true,true,product(inverse(d),multiply(c,b),c),true) = true,
inference(paramodulation,[status(thm)],[f6170,f707]) ).
fof(f23521,plain,
product(inverse(d),multiply(c,b),c) = true,
inference(forward_demodulation,[status(thm)],[f20,f23520]) ).
fof(f24212,plain,
ifeq(true,true,product(d,c,multiply(c,b)),true) = true,
inference(paramodulation,[status(thm)],[f23521,f856]) ).
fof(f24213,plain,
product(d,c,multiply(c,b)) = true,
inference(forward_demodulation,[status(thm)],[f20,f24212]) ).
fof(f24507,plain,
ifeq2(true,true,multiply(c,b),multiply(d,c)) = multiply(d,c),
inference(paramodulation,[status(thm)],[f24213,f54]) ).
fof(f24508,plain,
multiply(c,b) = multiply(d,c),
inference(forward_demodulation,[status(thm)],[f19,f24507]) ).
fof(f27892,plain,
! [X0] : ifeq(true,true,product(h,multiply(b,X0),multiply(d,X0)),true) = true,
inference(paramodulation,[status(thm)],[f18129,f4864]) ).
fof(f27893,plain,
! [X0] : product(h,multiply(b,X0),multiply(d,X0)) = true,
inference(forward_demodulation,[status(thm)],[f20,f27892]) ).
fof(f28455,plain,
! [X0] : ifeq2(true,true,multiply(d,X0),multiply(h,multiply(b,X0))) = multiply(h,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f27893,f54]) ).
fof(f28456,plain,
! [X0] : multiply(d,X0) = multiply(h,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f19,f28455]) ).
fof(f38296,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)],[f20182,f54]) ).
fof(f38297,plain,
! [X0] : d = multiply(multiply(c,X0),inverse(multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f19,f38296]) ).
fof(f38968,plain,
d = multiply(inverse(c),inverse(multiply(a,c))),
inference(paramodulation,[status(thm)],[f1340,f38297]) ).
fof(f38969,plain,
d = inverse(multiply(multiply(a,c),c)),
inference(forward_demodulation,[status(thm)],[f8276,f38968]) ).
fof(f39052,plain,
inverse(multiply(a,c)) = multiply(c,d),
inference(paramodulation,[status(thm)],[f38969,f7041]) ).
fof(f43797,plain,
ifeq(true,true,product(a,c,multiply(inverse(a),b)),true) = true,
inference(paramodulation,[status(thm)],[f1483,f1360]) ).
fof(f43798,plain,
product(a,c,multiply(inverse(a),b)) = true,
inference(forward_demodulation,[status(thm)],[f20,f43797]) ).
fof(f45102,plain,
ifeq2(true,true,multiply(inverse(a),b),multiply(a,c)) = multiply(a,c),
inference(paramodulation,[status(thm)],[f43798,f54]) ).
fof(f45103,plain,
multiply(inverse(a),b) = multiply(a,c),
inference(forward_demodulation,[status(thm)],[f19,f45102]) ).
fof(f45355,plain,
! [X0,X1] : ifeq(true,true,product(X0,multiply(X0,X1),multiply(inverse(X0),X1)),true) = true,
inference(paramodulation,[status(thm)],[f1483,f1379]) ).
fof(f45356,plain,
! [X0,X1] : product(X0,multiply(X0,X1),multiply(inverse(X0),X1)) = true,
inference(forward_demodulation,[status(thm)],[f20,f45355]) ).
fof(f45357,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(f45358,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)) = true,
inference(forward_demodulation,[status(thm)],[f20,f45357]) ).
fof(f45749,plain,
inverse(inverse(a)) = multiply(b,inverse(multiply(a,c))),
inference(paramodulation,[status(thm)],[f45103,f7041]) ).
fof(f45750,plain,
a = multiply(b,inverse(multiply(a,c))),
inference(forward_demodulation,[status(thm)],[f1076,f45749]) ).
fof(f45751,plain,
a = multiply(b,multiply(c,d)),
inference(forward_demodulation,[status(thm)],[f39052,f45750]) ).
fof(f45819,plain,
multiply(d,multiply(c,d)) = multiply(h,a),
inference(paramodulation,[status(thm)],[f45751,f28456]) ).
fof(f47194,plain,
! [X0,X1] : ifeq2(true,true,multiply(inverse(X0),X1),multiply(X0,multiply(X0,X1))) = multiply(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f45356,f54]) ).
fof(f47195,plain,
! [X0,X1] : multiply(inverse(X0),X1) = multiply(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f47194]) ).
fof(f48558,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),inverse(X1)) = multiply(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f7006,f47195]) ).
fof(f48559,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,X0))) = multiply(multiply(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f8276,f48558]) ).
fof(f58544,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)],[f45358,f54]) ).
fof(f58545,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f19,f58544]) ).
fof(f61440,plain,
! [X0,X1] : inverse(multiply(X0,multiply(X1,X0))) = multiply(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f58545,f48559]) ).
fof(f61648,plain,
inverse(multiply(c,multiply(c,b))) = multiply(d,multiply(c,d)),
inference(paramodulation,[status(thm)],[f24508,f61440]) ).
fof(f61649,plain,
inverse(multiply(inverse(c),b)) = multiply(d,multiply(c,d)),
inference(forward_demodulation,[status(thm)],[f47195,f61648]) ).
fof(f61650,plain,
multiply(inverse(b),c) = multiply(d,multiply(c,d)),
inference(forward_demodulation,[status(thm)],[f8393,f61649]) ).
fof(f61651,plain,
multiply(inverse(b),c) = multiply(h,a),
inference(forward_demodulation,[status(thm)],[f45819,f61650]) ).
fof(f62439,plain,
inverse(inverse(b)) = multiply(c,inverse(multiply(h,a))),
inference(paramodulation,[status(thm)],[f61651,f7041]) ).
fof(f62440,plain,
b = multiply(c,inverse(multiply(h,a))),
inference(forward_demodulation,[status(thm)],[f1076,f62439]) ).
fof(f62441,plain,
b = k,
inference(forward_demodulation,[status(thm)],[f16146,f62440]) ).
fof(f62595,plain,
product(b,inverse(b),identity) != true,
inference(backward_demodulation,[status(thm)],[f62441,f36]) ).
fof(f62596,plain,
true != true,
inference(forward_demodulation,[status(thm)],[f24,f62595]) ).
fof(f62597,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f62596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP002-10 : TPTP v8.1.2. Released v7.3.0.
% 0.11/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 11:45:43 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 13.22/2.02 % Refutation found
% 13.22/2.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.22/2.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.80/2.11 % Elapsed time: 1.760739 seconds
% 13.80/2.11 % CPU time: 13.703629 seconds
% 13.80/2.11 % Memory used: 284.297 MB
%------------------------------------------------------------------------------