TSTP Solution File: GRP682+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP682+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : Wed May 31 12:12:32 EDT 2023
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 10
% Syntax : Number of formulae : 118 ( 99 unt; 0 def)
% Number of atoms : 137 ( 118 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 19 ~; 15 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 240 (; 231 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : ld(A,mult(A,A)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [D,C,B,A] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [D,C,B,A] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [X0,X1,X2] :
( ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2))
& ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2))
& ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f13,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f16,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ld(ld(X0,X1),mult(ld(X0,X1),X2)) != ld(X0,mult(X0,X2))
| ld(rd(X0,X1),mult(rd(X0,X1),X2)) != ld(X0,mult(X0,X2)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f18,plain,
( ? [X0,X1,X2] : ld(ld(X0,X1),mult(ld(X0,X1),X2)) != ld(X0,mult(X0,X2))
| ? [X0,X1,X2] : ld(rd(X0,X1),mult(rd(X0,X1),X2)) != ld(X0,mult(X0,X2)) ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f19,plain,
( ld(ld(sk0_0,sk0_1),mult(ld(sk0_0,sk0_1),sk0_2)) != ld(sk0_0,mult(sk0_0,sk0_2))
| ld(rd(sk0_3,sk0_4),mult(rd(sk0_3,sk0_4),sk0_5)) != ld(sk0_3,mult(sk0_3,sk0_5)) ),
inference(skolemization,[status(esa)],[f18]) ).
fof(f20,plain,
( ld(ld(sk0_0,sk0_1),mult(ld(sk0_0,sk0_1),sk0_2)) != ld(sk0_0,mult(sk0_0,sk0_2))
| ld(rd(sk0_3,sk0_4),mult(rd(sk0_3,sk0_4),sk0_5)) != ld(sk0_3,mult(sk0_3,sk0_5)) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
( spl0_0
<=> ld(ld(sk0_0,sk0_1),mult(ld(sk0_0,sk0_1),sk0_2)) = ld(sk0_0,mult(sk0_0,sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f23,plain,
( ld(ld(sk0_0,sk0_1),mult(ld(sk0_0,sk0_1),sk0_2)) != ld(sk0_0,mult(sk0_0,sk0_2))
| spl0_0 ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( spl0_1
<=> ld(rd(sk0_3,sk0_4),mult(rd(sk0_3,sk0_4),sk0_5)) = ld(sk0_3,mult(sk0_3,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f26,plain,
( ld(rd(sk0_3,sk0_4),mult(rd(sk0_3,sk0_4),sk0_5)) != ld(sk0_3,mult(sk0_3,sk0_5))
| spl0_1 ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f20,f21,f24]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f12,f14]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f12,f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(forward_demodulation,[status(thm)],[f13,f15]) ).
fof(f31,plain,
! [X0,X1,X2,X3] : mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(forward_demodulation,[status(thm)],[f13,f30]) ).
fof(f32,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(forward_demodulation,[status(thm)],[f12,f16]) ).
fof(f33,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(forward_demodulation,[status(thm)],[f13,f32]) ).
fof(f34,plain,
( mult(ld(sk0_0,sk0_1),ld(ld(sk0_0,sk0_1),sk0_2)) != ld(sk0_0,mult(sk0_0,sk0_2))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f12,f23]) ).
fof(f35,plain,
( mult(ld(sk0_0,sk0_1),ld(ld(sk0_0,sk0_1),sk0_2)) != mult(sk0_0,ld(sk0_0,sk0_2))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f12,f34]) ).
fof(f36,plain,
! [X0] : mult(X0,ld(X0,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f12,f10]) ).
fof(f37,plain,
! [X0] : mult(rd(X0,X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f13,f11]) ).
fof(f39,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f36,f12]) ).
fof(f40,plain,
! [X0] : mult(rd(rd(X0,X0),X0),X0) = rd(X0,X0),
inference(paramodulation,[status(thm)],[f37,f13]) ).
fof(f41,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f33,f40]) ).
fof(f42,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f39,f41]) ).
fof(f43,plain,
! [X0] : mult(rd(X0,ld(X0,X0)),ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(paramodulation,[status(thm)],[f36,f13]) ).
fof(f44,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(backward_demodulation,[status(thm)],[f42,f37]) ).
fof(f47,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = mult(rd(ld(X0,X0),X1),X1),
inference(backward_demodulation,[status(thm)],[f42,f33]) ).
fof(f48,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(ld(X0,mult(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f12,f29]) ).
fof(f49,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f12,f48]) ).
fof(f55,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(mult(X0,ld(X0,X2)),ld(X2,X2)),
inference(paramodulation,[status(thm)],[f36,f29]) ).
fof(f70,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = mult(ld(ld(X0,X0),ld(X0,X0)),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f42,f47]) ).
fof(f71,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f44,f70]) ).
fof(f106,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(ld(X0,X0),X2),X2)),
inference(paramodulation,[status(thm)],[f36,f31]) ).
fof(f107,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(X0,ld(X0,ld(X2,X2)))),
inference(forward_demodulation,[status(thm)],[f47,f106]) ).
fof(f155,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
inference(paramodulation,[status(thm)],[f55,f12]) ).
fof(f196,plain,
! [X0,X1,X2] : mult(X0,ld(mult(X0,ld(X0,X0)),mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f36,f49]) ).
fof(f197,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,X2))) = mult(mult(X0,ld(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f36,f196]) ).
fof(f298,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
inference(paramodulation,[status(thm)],[f44,f49]) ).
fof(f299,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(mult(X0,ld(X0,ld(X2,X2))),X2),
inference(forward_demodulation,[status(thm)],[f197,f298]) ).
fof(f300,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,mult(ld(X2,X2),X2))),
inference(forward_demodulation,[status(thm)],[f197,f299]) ).
fof(f301,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f44,f300]) ).
fof(f325,plain,
! [X0,X1] : mult(mult(X0,ld(X0,X0)),ld(X0,X1)) = mult(X0,ld(X0,X1)),
inference(paramodulation,[status(thm)],[f49,f36]) ).
fof(f326,plain,
! [X0,X1] : mult(X0,ld(X0,mult(X0,ld(X0,X1)))) = mult(X0,ld(X0,X1)),
inference(forward_demodulation,[status(thm)],[f197,f325]) ).
fof(f327,plain,
! [X0,X1] : mult(X0,mult(X0,ld(X0,ld(X0,X1)))) = mult(X0,ld(X0,X1)),
inference(forward_demodulation,[status(thm)],[f12,f326]) ).
fof(f340,plain,
! [X0,X1,X2,X3] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
inference(paramodulation,[status(thm)],[f49,f12]) ).
fof(f341,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),mult(X2,X3)))))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
inference(forward_demodulation,[status(thm)],[f197,f340]) ).
fof(f342,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(mult(X0,ld(X0,X2)),X3)),
inference(forward_demodulation,[status(thm)],[f301,f341]) ).
fof(f343,plain,
! [X0,X1,X2,X3] : mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),mult(X2,X3)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f197,f342]) ).
fof(f346,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,mult(X2,ld(X2,X2)))),
inference(backward_demodulation,[status(thm)],[f197,f55]) ).
fof(f347,plain,
! [X0,X1,X2] : mult(ld(X0,X1),ld(ld(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f36,f346]) ).
fof(f395,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(X1,X1))))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
inference(backward_demodulation,[status(thm)],[f197,f155]) ).
fof(f396,plain,
! [X0,X1,X2] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(ld(X0,X2),ld(ld(X0,X2),X1))),
inference(forward_demodulation,[status(thm)],[f301,f395]) ).
fof(f397,plain,
! [X0,X1] : mult(X0,ld(X0,ld(X1,X1))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f347,f396]) ).
fof(f427,plain,
( mult(sk0_0,ld(sk0_0,sk0_2)) != mult(sk0_0,ld(sk0_0,sk0_2))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f347,f35]) ).
fof(f428,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f427]) ).
fof(f429,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f437,plain,
( mult(rd(sk0_3,sk0_4),ld(rd(sk0_3,sk0_4),sk0_5)) != ld(sk0_3,mult(sk0_3,sk0_5))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f12,f26]) ).
fof(f438,plain,
( mult(rd(sk0_3,sk0_4),ld(rd(sk0_3,sk0_4),sk0_5)) != mult(sk0_3,ld(sk0_3,sk0_5))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f12,f437]) ).
fof(f455,plain,
! [X0,X1] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f71,f197]) ).
fof(f456,plain,
! [X0,X1] : mult(X0,ld(X0,ld(ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f301,f455]) ).
fof(f457,plain,
! [X0,X1] : mult(X0,ld(X0,ld(mult(X0,ld(X0,ld(X1,X1))),ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f397,f456]) ).
fof(f458,plain,
! [X0,X1] : mult(X0,ld(X0,ld(mult(X0,ld(X0,ld(X1,X1))),mult(X0,ld(X0,ld(X1,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f397,f457]) ).
fof(f459,plain,
! [X0,X1] : mult(X0,ld(X0,mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f397,f458]) ).
fof(f460,plain,
! [X0,X1] : mult(X0,mult(X0,ld(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f12,f459]) ).
fof(f461,plain,
! [X0,X1] : mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f327,f460]) ).
fof(f462,plain,
! [X0,X1] : mult(X0,ld(X0,ld(ld(X1,X1),ld(X1,X1)))) = mult(X0,ld(X0,ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f397,f461]) ).
fof(f482,plain,
! [X0,X1] : mult(X0,ld(X0,mult(X0,X1))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f36,f197]) ).
fof(f483,plain,
! [X0,X1] : mult(X0,mult(X0,ld(X0,X1))) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f12,f482]) ).
fof(f516,plain,
! [X0,X1,X2] : mult(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2)) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(paramodulation,[status(thm)],[f197,f12]) ).
fof(f517,plain,
! [X0,X1,X2] : mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),X2)))) = ld(mult(X0,ld(X0,X1)),mult(X0,ld(X0,mult(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f197,f516]) ).
fof(f518,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,ld(X0,X2)),mult(X0,ld(X0,mult(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f301,f517]) ).
fof(f519,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = mult(X0,ld(X0,ld(mult(X0,ld(X0,X2)),mult(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f343,f518]) ).
fof(f525,plain,
! [X0,X1,X2] : mult(rd(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X2,X2)),
inference(backward_demodulation,[status(thm)],[f483,f107]) ).
fof(f559,plain,
! [X0,X1] : ld(X0,X1) = mult(X0,ld(X0,ld(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f347]) ).
fof(f592,plain,
! [X0,X1,X2] : ld(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,ld(mult(X0,ld(X0,X1)),ld(mult(X0,ld(X0,X1)),X2))))),
inference(paramodulation,[status(thm)],[f197,f559]) ).
fof(f593,plain,
! [X0,X1,X2] : ld(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,ld(mult(X0,ld(X0,X1)),X2))),
inference(forward_demodulation,[status(thm)],[f301,f592]) ).
fof(f608,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,ld(X0,X2)),mult(X2,X1)),
inference(backward_demodulation,[status(thm)],[f593,f519]) ).
fof(f695,plain,
! [X0,X1] : mult(ld(rd(X0,X1),rd(X0,X1)),rd(X0,X1)) = mult(rd(X0,X1),ld(X1,X1)),
inference(paramodulation,[status(thm)],[f42,f525]) ).
fof(f696,plain,
! [X0,X1] : rd(X0,X1) = mult(rd(X0,X1),ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f44,f695]) ).
fof(f703,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),rd(X1,X1)) = mult(X0,ld(X1,X1)),
inference(paramodulation,[status(thm)],[f42,f525]) ).
fof(f704,plain,
! [X0,X1] : mult(rd(X0,ld(X1,X1)),ld(X1,X1)) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f42,f703]) ).
fof(f727,plain,
! [X0] : mult(X0,ld(X0,X0)) = rd(X0,ld(X0,X0)),
inference(backward_demodulation,[status(thm)],[f704,f43]) ).
fof(f728,plain,
! [X0] : X0 = rd(X0,ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f36,f727]) ).
fof(f748,plain,
! [X0,X1] : mult(rd(X0,rd(X1,ld(X1,X1))),X1) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
inference(paramodulation,[status(thm)],[f728,f525]) ).
fof(f749,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(ld(X1,X1),ld(X1,X1))),
inference(forward_demodulation,[status(thm)],[f728,f748]) ).
fof(f764,plain,
! [X0] : rd(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f42,f696]) ).
fof(f765,plain,
! [X0] : ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f42,f764]) ).
fof(f776,plain,
! [X0] : mult(rd(ld(X0,X0),ld(X0,X0)),ld(X0,X0)) = rd(ld(X0,X0),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f765,f13]) ).
fof(f777,plain,
! [X0] : mult(X0,ld(X0,ld(ld(X0,X0),ld(X0,X0)))) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f47,f776]) ).
fof(f778,plain,
! [X0] : mult(X0,ld(X0,ld(X0,X0))) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f462,f777]) ).
fof(f779,plain,
! [X0] : ld(X0,X0) = rd(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f559,f778]) ).
fof(f780,plain,
! [X0] : ld(X0,X0) = ld(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f42,f779]) ).
fof(f784,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(backward_demodulation,[status(thm)],[f780,f749]) ).
fof(f1244,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,mult(X0,ld(X0,X2))),mult(mult(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f12,f608]) ).
fof(f1245,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = ld(mult(X0,X2),mult(mult(X0,X2),X1)),
inference(forward_demodulation,[status(thm)],[f483,f1244]) ).
fof(f1246,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = mult(mult(X0,X2),ld(mult(X0,X2),X1)),
inference(forward_demodulation,[status(thm)],[f12,f1245]) ).
fof(f2473,plain,
! [X0,X1,X2] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(mult(X0,ld(X1,X1)),ld(mult(rd(X0,X1),X1),X2)),
inference(paramodulation,[status(thm)],[f784,f1246]) ).
fof(f2474,plain,
! [X0,X1,X2] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(mult(X0,ld(X1,X1)),ld(mult(X0,ld(X1,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f784,f2473]) ).
fof(f2475,plain,
! [X0,X1,X2] : mult(rd(X0,X1),ld(rd(X0,X1),X2)) = mult(X0,ld(X0,X2)),
inference(forward_demodulation,[status(thm)],[f1246,f2474]) ).
fof(f2633,plain,
( mult(sk0_3,ld(sk0_3,sk0_5)) != mult(sk0_3,ld(sk0_3,sk0_5))
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f2475,f438]) ).
fof(f2634,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f2633]) ).
fof(f2635,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2634]) ).
fof(f2636,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f429,f2635]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : GRP682+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n016.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 11:59:59 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.112439 seconds
% 0.13/0.41 % CPU time: 0.420142 seconds
% 0.13/0.41 % Memory used: 42.961 MB
%------------------------------------------------------------------------------