TSTP Solution File: RNG004-10 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG004-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 20:37:39 EDT 2024
% Result : Unsatisfiable 50.49s 6.75s
% Output : CNFRefutation 52.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 18
% Syntax : Number of formulae : 161 ( 161 unt; 0 def)
% Number of atoms : 161 ( 160 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 288 ( 288 !; 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] : sum(additive_identity,X,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : sum(X,Y,add(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,Z,W,Y,V,X] : ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,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(f14,axiom,
! [X,V3,V4,Z,V2,Y,V1] : ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [V3,X,V4,Z,V2,Y,V1] : ifeq(product(V3,X,V4),true,ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,V,U] : ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,V,U] : ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
product(a,b,c) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(additive_inverse(a),additive_inverse(b),d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f25,plain,
! [X0] : sum(additive_identity,X0,X0) = true,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f27,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f29,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity) = true,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f30,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity) = true,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f35,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)],[f13]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X1,X6),true,ifeq(sum(X5,X3,X0),true,sum(X6,X4,X2),true),true),true),true) = true,
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f41,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)],[f19]) ).
fof(f42,plain,
product(a,b,c) = true,
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f43,plain,
product(additive_inverse(a),additive_inverse(b),d) = true,
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f44,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f51,plain,
! [X0,X1] : true = ifeq(true,true,sum(X0,X1,add(X1,X0)),true),
inference(paramodulation,[status(thm)],[f28,f33]) ).
fof(f61,plain,
! [X0,X1] : true = sum(X0,X1,add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f24,f51]) ).
fof(f67,plain,
! [X0,X1,X2,X3] : true = ifeq(true,true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),true),
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f88,plain,
! [X0,X1,X2,X3] : true = ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),
inference(forward_demodulation,[status(thm)],[f24,f67]) ).
fof(f162,plain,
! [X0,X1] : X0 = ifeq2(true,true,ifeq2(sum(additive_identity,X0,X1),true,X1,X0),X0),
inference(paramodulation,[status(thm)],[f25,f40]) ).
fof(f166,plain,
! [X0,X1,X2] : add(X0,X1) = ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f40]) ).
fof(f167,plain,
! [X0,X1] : X0 = ifeq2(sum(additive_inverse(X1),X1,X0),true,ifeq2(true,true,additive_identity,X0),X0),
inference(paramodulation,[status(thm)],[f29,f40]) ).
fof(f170,plain,
! [X0,X1] : X0 = ifeq2(sum(X1,additive_identity,X0),true,ifeq2(true,true,X1,X0),X0),
inference(paramodulation,[status(thm)],[f26,f40]) ).
fof(f171,plain,
! [X0,X1,X2] : X0 = ifeq2(sum(X1,X2,X0),true,ifeq2(true,true,add(X2,X1),X0),X0),
inference(paramodulation,[status(thm)],[f61,f40]) ).
fof(f174,plain,
! [X0,X1] : X0 = ifeq2(sum(additive_identity,X0,X1),true,X1,X0),
inference(forward_demodulation,[status(thm)],[f23,f162]) ).
fof(f178,plain,
! [X0,X1,X2] : add(X0,X1) = ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f166]) ).
fof(f179,plain,
! [X0,X1] : X0 = ifeq2(sum(additive_inverse(X1),X1,X0),true,additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f23,f167]) ).
fof(f182,plain,
! [X0,X1] : X0 = ifeq2(sum(X1,additive_identity,X0),true,X1,X0),
inference(forward_demodulation,[status(thm)],[f23,f170]) ).
fof(f183,plain,
! [X0,X1,X2] : X0 = ifeq2(sum(X1,X2,X0),true,add(X2,X1),X0),
inference(forward_demodulation,[status(thm)],[f23,f171]) ).
fof(f186,plain,
additive_inverse(additive_identity) = ifeq2(true,true,additive_identity,additive_inverse(additive_identity)),
inference(paramodulation,[status(thm)],[f30,f174]) ).
fof(f188,plain,
! [X0] : X0 = ifeq2(true,true,add(X0,additive_identity),X0),
inference(paramodulation,[status(thm)],[f61,f174]) ).
fof(f191,plain,
additive_inverse(additive_identity) = additive_identity,
inference(forward_demodulation,[status(thm)],[f23,f186]) ).
fof(f192,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f23,f188]) ).
fof(f240,plain,
! [X0,X1,X2,X3,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(true,true,ifeq(product(X3,X0,X4),true,product(X4,X1,multiply(X3,X2)),true),true),true),
inference(paramodulation,[status(thm)],[f27,f35]) ).
fof(f253,plain,
! [X0,X1,X2,X3,X4] : true = ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,product(X4,X1,multiply(X3,X2)),true),true),
inference(forward_demodulation,[status(thm)],[f24,f240]) ).
fof(f258,plain,
! [X0,X1,X2,X3] : true = ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,X0,b),true,sum(X3,X1,c),true),true),true),true),
inference(paramodulation,[status(thm)],[f42,f36]) ).
fof(f261,plain,
! [X0,X1,X2,X3] : true = ifeq(product(a,X0,X1),true,ifeq(true,true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,b,X0),true,sum(X3,c,X1),true),true),true),true),
inference(paramodulation,[status(thm)],[f42,f36]) ).
fof(f280,plain,
! [X0,X1,X2,X3] : true = ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,X0,b),true,sum(X3,X1,c),true),true),true),
inference(forward_demodulation,[status(thm)],[f24,f258]) ).
fof(f283,plain,
! [X0,X1,X2,X3] : true = ifeq(product(a,X0,X1),true,ifeq(product(a,X2,X3),true,ifeq(sum(X2,b,X0),true,sum(X3,c,X1),true),true),true),
inference(forward_demodulation,[status(thm)],[f24,f261]) ).
fof(f426,plain,
! [X0] : add(X0,additive_inverse(X0)) = ifeq2(true,true,additive_identity,add(X0,additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f61,f179]) ).
fof(f431,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(forward_demodulation,[status(thm)],[f23,f426]) ).
fof(f488,plain,
! [X0,X1,X2,X3] : true = ifeq(true,true,ifeq(product(X0,additive_inverse(b),X1),true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,X0,additive_inverse(a)),true,sum(X3,X1,d),true),true),true),true),
inference(paramodulation,[status(thm)],[f43,f38]) ).
fof(f492,plain,
! [X0,X1,X2,X3] : true = ifeq(product(X0,additive_inverse(b),X1),true,ifeq(true,true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,additive_inverse(a),X0),true,sum(X3,d,X1),true),true),true),true),
inference(paramodulation,[status(thm)],[f43,f38]) ).
fof(f514,plain,
! [X0,X1,X2,X3] : true = ifeq(product(X0,additive_inverse(b),X1),true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,X0,additive_inverse(a)),true,sum(X3,X1,d),true),true),true),
inference(forward_demodulation,[status(thm)],[f24,f488]) ).
fof(f518,plain,
! [X0,X1,X2,X3] : true = ifeq(product(X0,additive_inverse(b),X1),true,ifeq(product(X2,additive_inverse(b),X3),true,ifeq(sum(X2,additive_inverse(a),X0),true,sum(X3,d,X1),true),true),true),
inference(forward_demodulation,[status(thm)],[f24,f492]) ).
fof(f766,plain,
! [X0,X1] : add(X0,X1) = ifeq2(true,true,add(X1,X0),add(X0,X1)),
inference(paramodulation,[status(thm)],[f28,f183]) ).
fof(f776,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f23,f766]) ).
fof(f797,plain,
! [X0,X1,X2] : multiply(X0,X1) = ifeq2(true,true,ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f41]) ).
fof(f809,plain,
! [X0,X1,X2] : multiply(X0,X1) = ifeq2(product(X0,X1,X2),true,X2,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f797]) ).
fof(f1945,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,b),true,sum(X1,c,c),true),true),true),
inference(paramodulation,[status(thm)],[f42,f280]) ).
fof(f1957,plain,
! [X0,X1] : true = ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,b),true,sum(X1,c,c),true),true),
inference(forward_demodulation,[status(thm)],[f24,f1945]) ).
fof(f2012,plain,
! [X0,X1,X2] : true = ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,X2),true,sum(X1,c,multiply(a,X2)),true),true),true),
inference(paramodulation,[status(thm)],[f27,f283]) ).
fof(f2029,plain,
! [X0,X1,X2] : true = ifeq(product(a,X0,X1),true,ifeq(sum(X0,b,X2),true,sum(X1,c,multiply(a,X2)),true),true),
inference(forward_demodulation,[status(thm)],[f24,f2012]) ).
fof(f2916,plain,
! [X0,X1] : true = ifeq(product(X0,additive_inverse(b),X1),true,ifeq(true,true,ifeq(sum(additive_inverse(a),X0,additive_inverse(a)),true,sum(d,X1,d),true),true),true),
inference(paramodulation,[status(thm)],[f43,f514]) ).
fof(f2926,plain,
! [X0,X1] : true = ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(additive_inverse(a),X0,additive_inverse(a)),true,sum(d,X1,d),true),true),
inference(forward_demodulation,[status(thm)],[f24,f2916]) ).
fof(f2980,plain,
! [X0,X1,X2] : true = ifeq(true,true,ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(X0,additive_inverse(a),X2),true,sum(X1,d,multiply(X2,additive_inverse(b))),true),true),true),
inference(paramodulation,[status(thm)],[f27,f518]) ).
fof(f2996,plain,
! [X0,X1,X2] : true = ifeq(product(X0,additive_inverse(b),X1),true,ifeq(sum(X0,additive_inverse(a),X2),true,sum(X1,d,multiply(X2,additive_inverse(b))),true),true),
inference(forward_demodulation,[status(thm)],[f24,f2980]) ).
fof(f3726,plain,
! [X0,X1,X2] : true = ifeq(sum(X0,X1,X2),true,ifeq(true,true,sum(additive_inverse(X0),X2,X1),true),true),
inference(paramodulation,[status(thm)],[f29,f88]) ).
fof(f3746,plain,
! [X0,X1,X2] : true = ifeq(sum(X0,X1,X2),true,sum(additive_inverse(X0),X2,X1),true),
inference(forward_demodulation,[status(thm)],[f24,f3726]) ).
fof(f4179,plain,
! [X0] : true = ifeq(true,true,sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),true),
inference(paramodulation,[status(thm)],[f29,f3746]) ).
fof(f4183,plain,
! [X0,X1] : true = ifeq(true,true,sum(additive_inverse(X0),add(X1,X0),X1),true),
inference(paramodulation,[status(thm)],[f61,f3746]) ).
fof(f4184,plain,
! [X0,X1] : true = ifeq(true,true,sum(additive_inverse(X0),add(X0,X1),X1),true),
inference(paramodulation,[status(thm)],[f28,f3746]) ).
fof(f4202,plain,
! [X0] : true = sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f24,f4179]) ).
fof(f4207,plain,
! [X0,X1] : true = sum(additive_inverse(X0),add(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f24,f4183]) ).
fof(f4208,plain,
! [X0,X1] : true = sum(additive_inverse(X0),add(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f24,f4184]) ).
fof(f4219,plain,
! [X0] : X0 = ifeq2(true,true,additive_inverse(additive_inverse(X0)),X0),
inference(paramodulation,[status(thm)],[f4202,f182]) ).
fof(f4335,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f23,f4219]) ).
fof(f4982,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = ifeq2(true,true,X1,add(additive_inverse(X0),add(X1,X0))),
inference(paramodulation,[status(thm)],[f4207,f178]) ).
fof(f5104,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f23,f4982]) ).
fof(f5530,plain,
! [X0,X1] : X0 = add(X1,add(X0,additive_inverse(X1))),
inference(paramodulation,[status(thm)],[f4335,f5104]) ).
fof(f5532,plain,
! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f5104,f5104]) ).
fof(f5536,plain,
! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
inference(paramodulation,[status(thm)],[f776,f5104]) ).
fof(f5584,plain,
! [X0,X1] : true = sum(add(X0,additive_inverse(X1)),X1,X0),
inference(paramodulation,[status(thm)],[f5530,f61]) ).
fof(f5800,plain,
! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f5536,f5104]) ).
fof(f7791,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X1,X0))),
inference(forward_demodulation,[status(thm)],[f776,f5532]) ).
fof(f7794,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X1),additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f5104,f7791]) ).
fof(f7797,plain,
! [X0,X1] : additive_inverse(add(X0,additive_inverse(X1))) = add(X1,additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f5530,f7791]) ).
fof(f7810,plain,
! [X0,X1] : true = sum(additive_inverse(X0),additive_inverse(X1),additive_inverse(add(X0,X1))),
inference(paramodulation,[status(thm)],[f7791,f4208]) ).
fof(f9050,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(forward_demodulation,[status(thm)],[f776,f5800]) ).
fof(f17639,plain,
! [X0,X1] : additive_identity = add(add(X0,additive_inverse(X1)),add(X1,additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f7797,f431]) ).
fof(f23450,plain,
! [X0,X1] : add(additive_inverse(X0),additive_inverse(X1)) = ifeq2(true,true,additive_inverse(add(X0,X1)),add(additive_inverse(X0),additive_inverse(X1))),
inference(paramodulation,[status(thm)],[f7810,f178]) ).
fof(f23681,plain,
! [X1,X0] : additive_inverse(add(X1,X0)) = ifeq2(true,true,additive_inverse(add(X0,X1)),add(additive_inverse(X0),additive_inverse(X1))),
inference(forward_demodulation,[status(thm)],[f7794,f23450]) ).
fof(f23682,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = additive_inverse(add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f23,f23681]) ).
fof(f24351,plain,
! [X0,X1] : additive_identity = add(add(X0,X1),additive_inverse(add(X1,X0))),
inference(paramodulation,[status(thm)],[f23682,f431]) ).
fof(f46565,plain,
! [X0] : true = ifeq(product(a,add(b,additive_inverse(b)),X0),true,ifeq(true,true,sum(X0,c,c),true),true),
inference(paramodulation,[status(thm)],[f5584,f1957]) ).
fof(f46579,plain,
! [X0] : true = ifeq(product(a,additive_identity,X0),true,ifeq(true,true,sum(X0,c,c),true),true),
inference(forward_demodulation,[status(thm)],[f431,f46565]) ).
fof(f46580,plain,
! [X0] : true = ifeq(product(a,additive_identity,X0),true,sum(X0,c,c),true),
inference(forward_demodulation,[status(thm)],[f24,f46579]) ).
fof(f46800,plain,
true = ifeq(true,true,sum(multiply(a,additive_identity),c,c),true),
inference(paramodulation,[status(thm)],[f27,f46580]) ).
fof(f46811,plain,
true = sum(multiply(a,additive_identity),c,c),
inference(forward_demodulation,[status(thm)],[f24,f46800]) ).
fof(f46998,plain,
add(multiply(a,additive_identity),c) = ifeq2(true,true,c,add(multiply(a,additive_identity),c)),
inference(paramodulation,[status(thm)],[f46811,f178]) ).
fof(f47250,plain,
add(multiply(a,additive_identity),c) = c,
inference(forward_demodulation,[status(thm)],[f23,f46998]) ).
fof(f47280,plain,
add(c,multiply(a,additive_identity)) = c,
inference(forward_demodulation,[status(thm)],[f776,f47250]) ).
fof(f47336,plain,
additive_identity = add(c,additive_inverse(add(multiply(a,additive_identity),c))),
inference(paramodulation,[status(thm)],[f47280,f24351]) ).
fof(f47384,plain,
additive_identity = additive_inverse(multiply(a,additive_identity)),
inference(forward_demodulation,[status(thm)],[f9050,f47336]) ).
fof(f47407,plain,
! [X0] : additive_identity = add(add(X0,additive_identity),add(multiply(a,additive_identity),additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f47384,f17639]) ).
fof(f47512,plain,
! [X0] : additive_identity = add(X0,add(multiply(a,additive_identity),additive_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f192,f47407]) ).
fof(f47513,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[status(thm)],[f5530,f47512]) ).
fof(f47581,plain,
true = product(a,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f47513,f27]) ).
fof(f47810,plain,
! [X0,X1] : true = ifeq(product(additive_identity,X0,X1),true,ifeq(true,true,product(additive_identity,X0,multiply(a,X1)),true),true),
inference(paramodulation,[status(thm)],[f47581,f253]) ).
fof(f48033,plain,
! [X0,X1] : true = ifeq(product(additive_identity,X0,X1),true,product(additive_identity,X0,multiply(a,X1)),true),
inference(forward_demodulation,[status(thm)],[f24,f47810]) ).
fof(f49366,plain,
! [X0] : true = ifeq(product(a,additive_inverse(b),X0),true,ifeq(true,true,sum(X0,c,multiply(a,additive_identity)),true),true),
inference(paramodulation,[status(thm)],[f29,f2029]) ).
fof(f49391,plain,
! [X0] : true = ifeq(product(a,additive_inverse(b),X0),true,sum(X0,c,multiply(a,additive_identity)),true),
inference(forward_demodulation,[status(thm)],[f24,f49366]) ).
fof(f49392,plain,
! [X0] : true = ifeq(product(a,additive_inverse(b),X0),true,sum(X0,c,additive_identity),true),
inference(forward_demodulation,[status(thm)],[f47513,f49391]) ).
fof(f64287,plain,
! [X0] : true = ifeq(true,true,product(additive_identity,X0,multiply(a,multiply(additive_identity,X0))),true),
inference(paramodulation,[status(thm)],[f27,f48033]) ).
fof(f64296,plain,
! [X0] : true = product(additive_identity,X0,multiply(a,multiply(additive_identity,X0))),
inference(forward_demodulation,[status(thm)],[f24,f64287]) ).
fof(f64340,plain,
true = ifeq(true,true,ifeq(sum(additive_inverse(a),additive_identity,additive_inverse(a)),true,sum(d,multiply(a,multiply(additive_identity,additive_inverse(b))),d),true),true),
inference(paramodulation,[status(thm)],[f64296,f2926]) ).
fof(f64540,plain,
! [X0] : multiply(additive_identity,X0) = ifeq2(true,true,multiply(a,multiply(additive_identity,X0)),multiply(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f64296,f809]) ).
fof(f64598,plain,
true = ifeq(sum(additive_inverse(a),additive_identity,additive_inverse(a)),true,sum(d,multiply(a,multiply(additive_identity,additive_inverse(b))),d),true),
inference(forward_demodulation,[status(thm)],[f24,f64340]) ).
fof(f64599,plain,
true = ifeq(true,true,sum(d,multiply(a,multiply(additive_identity,additive_inverse(b))),d),true),
inference(forward_demodulation,[status(thm)],[f26,f64598]) ).
fof(f64600,plain,
true = sum(d,multiply(a,multiply(additive_identity,additive_inverse(b))),d),
inference(forward_demodulation,[status(thm)],[f24,f64599]) ).
fof(f64808,plain,
! [X0] : multiply(additive_identity,X0) = multiply(a,multiply(additive_identity,X0)),
inference(forward_demodulation,[status(thm)],[f23,f64540]) ).
fof(f65829,plain,
true = sum(d,multiply(additive_identity,additive_inverse(b)),d),
inference(forward_demodulation,[status(thm)],[f64808,f64600]) ).
fof(f66034,plain,
add(d,multiply(additive_identity,additive_inverse(b))) = ifeq2(true,true,d,add(d,multiply(additive_identity,additive_inverse(b)))),
inference(paramodulation,[status(thm)],[f65829,f178]) ).
fof(f66326,plain,
add(d,multiply(additive_identity,additive_inverse(b))) = d,
inference(forward_demodulation,[status(thm)],[f23,f66034]) ).
fof(f66434,plain,
additive_identity = add(d,additive_inverse(add(multiply(additive_identity,additive_inverse(b)),d))),
inference(paramodulation,[status(thm)],[f66326,f24351]) ).
fof(f66482,plain,
additive_identity = additive_inverse(multiply(additive_identity,additive_inverse(b))),
inference(forward_demodulation,[status(thm)],[f9050,f66434]) ).
fof(f66532,plain,
! [X0] : additive_identity = add(add(X0,additive_identity),add(multiply(additive_identity,additive_inverse(b)),additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f66482,f17639]) ).
fof(f66650,plain,
! [X0] : additive_identity = add(X0,add(multiply(additive_identity,additive_inverse(b)),additive_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f192,f66532]) ).
fof(f66651,plain,
additive_identity = multiply(additive_identity,additive_inverse(b)),
inference(forward_demodulation,[status(thm)],[f5530,f66650]) ).
fof(f67700,plain,
! [X0] : true = ifeq(product(additive_inverse(additive_inverse(a)),additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,multiply(additive_identity,additive_inverse(b))),true),true),
inference(paramodulation,[status(thm)],[f29,f2996]) ).
fof(f67734,plain,
! [X0] : true = ifeq(product(a,additive_inverse(b),X0),true,ifeq(true,true,sum(X0,d,multiply(additive_identity,additive_inverse(b))),true),true),
inference(forward_demodulation,[status(thm)],[f4335,f67700]) ).
fof(f67735,plain,
! [X0] : true = ifeq(product(a,additive_inverse(b),X0),true,sum(X0,d,multiply(additive_identity,additive_inverse(b))),true),
inference(forward_demodulation,[status(thm)],[f24,f67734]) ).
fof(f67736,plain,
! [X0] : true = ifeq(product(a,additive_inverse(b),X0),true,sum(X0,d,additive_identity),true),
inference(forward_demodulation,[status(thm)],[f66651,f67735]) ).
fof(f76596,plain,
true = ifeq(true,true,sum(multiply(a,additive_inverse(b)),c,additive_identity),true),
inference(paramodulation,[status(thm)],[f27,f49392]) ).
fof(f76613,plain,
true = sum(multiply(a,additive_inverse(b)),c,additive_identity),
inference(forward_demodulation,[status(thm)],[f24,f76596]) ).
fof(f76926,plain,
add(multiply(a,additive_inverse(b)),c) = ifeq2(true,true,additive_identity,add(multiply(a,additive_inverse(b)),c)),
inference(paramodulation,[status(thm)],[f76613,f178]) ).
fof(f77236,plain,
add(multiply(a,additive_inverse(b)),c) = additive_identity,
inference(forward_demodulation,[status(thm)],[f23,f76926]) ).
fof(f77268,plain,
add(c,multiply(a,additive_inverse(b))) = additive_identity,
inference(forward_demodulation,[status(thm)],[f776,f77236]) ).
fof(f77374,plain,
additive_inverse(c) = add(multiply(a,additive_inverse(b)),additive_inverse(additive_identity)),
inference(paramodulation,[status(thm)],[f77268,f9050]) ).
fof(f77436,plain,
additive_inverse(c) = add(multiply(a,additive_inverse(b)),additive_identity),
inference(forward_demodulation,[status(thm)],[f191,f77374]) ).
fof(f77437,plain,
additive_inverse(c) = multiply(a,additive_inverse(b)),
inference(forward_demodulation,[status(thm)],[f192,f77436]) ).
fof(f77524,plain,
true = product(a,additive_inverse(b),additive_inverse(c)),
inference(paramodulation,[status(thm)],[f77437,f27]) ).
fof(f98041,plain,
true = ifeq(true,true,sum(additive_inverse(c),d,additive_identity),true),
inference(paramodulation,[status(thm)],[f77524,f67736]) ).
fof(f98059,plain,
true = sum(additive_inverse(c),d,additive_identity),
inference(forward_demodulation,[status(thm)],[f24,f98041]) ).
fof(f98268,plain,
true = ifeq(true,true,sum(additive_inverse(additive_inverse(c)),additive_identity,d),true),
inference(paramodulation,[status(thm)],[f98059,f3746]) ).
fof(f98592,plain,
true = sum(additive_inverse(additive_inverse(c)),additive_identity,d),
inference(forward_demodulation,[status(thm)],[f24,f98268]) ).
fof(f98593,plain,
true = sum(c,additive_identity,d),
inference(forward_demodulation,[status(thm)],[f4335,f98592]) ).
fof(f98731,plain,
d = ifeq2(true,true,c,d),
inference(paramodulation,[status(thm)],[f98593,f182]) ).
fof(f98998,plain,
d = c,
inference(forward_demodulation,[status(thm)],[f23,f98731]) ).
fof(f98999,plain,
$false,
inference(resolution,[status(thm)],[f98998,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : RNG004-10 : TPTP v8.1.2. Released v7.5.0.
% 0.09/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n006.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Mon Apr 29 22:12:20 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.6.0
% 50.49/6.75 % Refutation found
% 50.49/6.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 50.49/6.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 52.47/7.00 % Elapsed time: 6.661197 seconds
% 52.47/7.00 % CPU time: 51.948027 seconds
% 52.47/7.00 % Total memory used: 776.488 MB
% 52.47/7.00 % Net memory used: 762.251 MB
%------------------------------------------------------------------------------