%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP683-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:15:35 AM UTC 2026
% Result : Unsatisfiable 1.60s 1.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 10
% Syntax : Number of formulae : 220 ( 212 unt; 2 def)
% Number of atoms : 228 ( 210 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 6 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 502 ( 0 sgn 502 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f8,negated_conjecture,
mult(x3,ld(x4,mult(x4,x5))) != mult(x3,x5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f10,definition,
( spl0_1
<=> mult(x3,ld(x4,mult(x4,x5))) = mult(x3,x5) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f12,plain,
( mult(x3,ld(x4,mult(x4,x5))) != mult(x3,x5)
| spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f13,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f8,f10]) ).
fof(f17,plain,
! [X0] : ld(X0,mult(X0,ld(X0,X0))) = rd(rd(mult(X0,X0),X0),X0),
inference(superposition,[],[f7,f4]) ).
fof(f20,plain,
! [X0] : rd(X0,X0) = ld(X0,mult(X0,ld(rd(X0,X0),rd(X0,X0)))),
inference(superposition,[],[f2,f7]) ).
fof(f21,plain,
! [X0,X1] : rd(mult(mult(rd(X0,X0),X1),X1),X1) = mult(ld(X0,mult(X0,ld(X1,X1))),X1),
inference(superposition,[],[f4,f7]) ).
fof(f22,plain,
! [X0] : rd(X0,X0) = ld(X0,mult(X0,ld(X0,X0))),
inference(forward_demodulation,[],[f17,f2]) ).
fof(f23,plain,
! [X0] : rd(X0,X0) = ld(X0,ld(X0,mult(X0,X0))),
inference(forward_demodulation,[],[f22,f3]) ).
fof(f24,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(forward_demodulation,[],[f23,f1]) ).
fof(f25,plain,
! [X0,X1] : rd(mult(mult(rd(X0,X0),X1),X1),X1) = mult(ld(X0,mult(X0,rd(X1,X1))),X1),
inference(backward_demodulation,[],[f21,f24]) ).
fof(f26,plain,
! [X0,X1] : rd(mult(rd(X0,X0),X1),X1) = ld(X0,mult(X0,rd(X1,X1))),
inference(backward_demodulation,[],[f7,f24]) ).
fof(f28,plain,
! [X0] : rd(X0,X0) = ld(X0,mult(X0,rd(rd(X0,X0),rd(X0,X0)))),
inference(backward_demodulation,[],[f20,f24]) ).
fof(f29,plain,
! [X0] : ld(X0,mult(X0,X0)) = mult(X0,rd(X0,X0)),
inference(superposition,[],[f3,f24]) ).
fof(f30,plain,
! [X0] : mult(X0,rd(X0,X0)) = X0,
inference(forward_demodulation,[],[f29,f1]) ).
fof(f40,plain,
! [X0] : mult(X0,rd(X0,X0)) = ld(X0,mult(X0,mult(X0,rd(rd(X0,X0),rd(X0,X0))))),
inference(superposition,[],[f3,f28]) ).
fof(f41,plain,
! [X0] : ld(X0,mult(X0,mult(X0,rd(rd(X0,X0),rd(X0,X0))))) = X0,
inference(forward_demodulation,[],[f40,f30]) ).
fof(f44,plain,
! [X2,X0,X1] : mult(ld(X0,mult(X0,X1)),X2) = ld(X0,mult(X0,mult(X1,X2))),
inference(superposition,[],[f5,f1]) ).
fof(f47,plain,
! [X2,X0,X1] : mult(ld(X0,mult(X0,X1)),X2) = ld(rd(X0,X0),mult(rd(X0,X0),mult(X1,X2))),
inference(superposition,[],[f5,f28]) ).
fof(f50,plain,
! [X2,X0,X1] : mult(ld(X1,mult(X1,X0)),rd(X0,X0)) = ld(ld(X1,X2),mult(ld(X1,X2),X0)),
inference(superposition,[],[f5,f30]) ).
fof(f58,plain,
! [X2,X0,X1] : mult(X0,X2) = ld(ld(X0,X1),mult(ld(X0,X1),mult(X0,X2))),
inference(superposition,[],[f5,f1]) ).
fof(f76,plain,
! [X2,X3,X0,X1] : ld(ld(X0,mult(X0,X2)),mult(ld(X0,mult(X0,X2)),X3)) = ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,ld(ld(X0,mult(X0,X2)),X3)))),
inference(superposition,[],[f3,f5]) ).
fof(f80,plain,
! [X0,X1] : rd(mult(mult(rd(X0,X0),X1),X1),X1) = ld(rd(X0,X0),mult(rd(X0,X0),mult(rd(X1,X1),X1))),
inference(backward_demodulation,[],[f25,f47]) ).
fof(f85,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,ld(ld(X0,mult(X0,X2)),X3)))) = ld(ld(X0,mult(X0,X2)),ld(rd(X0,X0),mult(rd(X0,X0),mult(X2,X3)))),
inference(backward_demodulation,[],[f76,f47]) ).
fof(f86,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = ld(rd(X0,X0),mult(rd(X0,X0),mult(X2,X3))),
inference(backward_demodulation,[],[f5,f47]) ).
fof(f95,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = ld(rd(X1,X1),mult(rd(X1,X1),mult(X0,rd(X0,X0)))),
inference(backward_demodulation,[],[f50,f47]) ).
fof(f100,plain,
! [X2,X0,X1] : ld(X0,mult(X0,mult(X1,X2))) = ld(rd(X0,X0),mult(rd(X0,X0),mult(X1,X2))),
inference(forward_demodulation,[],[f44,f47]) ).
fof(f102,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = ld(rd(X1,X1),mult(rd(X1,X1),X0)),
inference(forward_demodulation,[],[f95,f30]) ).
fof(f109,plain,
! [X2,X0] : mult(X0,X2) = ld(rd(X0,X0),mult(rd(X0,X0),mult(X0,X2))),
inference(backward_demodulation,[],[f58,f86]) ).
fof(f125,plain,
! [X2,X3,X0] : ld(ld(X0,mult(X0,X2)),ld(rd(X0,X0),mult(rd(X0,X0),mult(X2,X3)))) = ld(rd(X0,X0),mult(rd(X0,X0),mult(X2,ld(ld(X0,mult(X0,X2)),X3)))),
inference(forward_demodulation,[],[f85,f86]) ).
fof(f130,plain,
! [X0,X1] : rd(mult(mult(rd(X0,X0),X1),X1),X1) = ld(rd(X0,X0),mult(rd(X0,X0),rd(mult(X1,X1),X1))),
inference(forward_demodulation,[],[f80,f4]) ).
fof(f134,plain,
! [X2,X0,X1] : mult(ld(X0,mult(X0,X1)),X2) = ld(X0,mult(X0,mult(X1,X2))),
inference(backward_demodulation,[],[f47,f100]) ).
fof(f154,plain,
! [X2,X0] : mult(X0,X2) = ld(X0,mult(X0,mult(X0,X2))),
inference(forward_demodulation,[],[f109,f100]) ).
fof(f155,plain,
! [X2,X3,X0] : ld(ld(X0,mult(X0,X2)),ld(rd(X0,X0),mult(rd(X0,X0),mult(X2,X3)))) = ld(X0,mult(X0,mult(X2,ld(ld(X0,mult(X0,X2)),X3)))),
inference(forward_demodulation,[],[f125,f100]) ).
fof(f160,plain,
! [X0,X1] : ld(rd(X0,X0),mult(rd(X0,X0),X1)) = rd(mult(mult(rd(X0,X0),X1),X1),X1),
inference(forward_demodulation,[],[f130,f2]) ).
fof(f171,plain,
! [X0] : mult(X0,rd(rd(X0,X0),rd(X0,X0))) = X0,
inference(backward_demodulation,[],[f41,f154]) ).
fof(f172,plain,
! [X2,X3,X0] : ld(ld(X0,mult(X0,X2)),ld(X0,mult(X0,mult(X2,X3)))) = ld(X0,mult(X0,mult(X2,ld(ld(X0,mult(X0,X2)),X3)))),
inference(forward_demodulation,[],[f155,f100]) ).
fof(f223,plain,
! [X2,X0,X1] : ld(ld(X0,mult(X0,X1)),mult(ld(X0,mult(X0,X1)),X2)) = ld(X0,mult(X0,mult(X1,ld(ld(X0,mult(X0,X1)),X2)))),
inference(superposition,[],[f3,f134]) ).
fof(f227,plain,
! [X2,X0,X1] : ld(ld(X0,mult(X0,X1)),mult(ld(X0,mult(X0,X1)),X2)) = ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,mult(X1,X2)))),
inference(forward_demodulation,[],[f223,f172]) ).
fof(f236,plain,
! [X2,X0,X1] : ld(rd(X0,X0),mult(rd(X0,X0),X2)) = ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,mult(X1,X2)))),
inference(forward_demodulation,[],[f227,f102]) ).
fof(f244,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,rd(mult(rd(rd(X0,X0),rd(X0,X0)),X2),X2)),
inference(superposition,[],[f6,f171]) ).
fof(f249,plain,
! [X2,X0,X1] : mult(X1,rd(mult(X2,X0),X0)) = rd(mult(mult(X1,X2),X0),X0),
inference(superposition,[],[f6,f2]) ).
fof(f267,plain,
! [X0,X1] : ld(rd(X0,X0),mult(rd(X0,X0),X1)) = mult(rd(X0,X0),rd(mult(X1,X1),X1)),
inference(backward_demodulation,[],[f160,f249]) ).
fof(f274,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(rd(X0,X0),mult(rd(X0,X0),rd(X2,X2)))),
inference(forward_demodulation,[],[f244,f26]) ).
fof(f280,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = ld(rd(X0,X0),mult(rd(X0,X0),X1)),
inference(forward_demodulation,[],[f267,f2]) ).
fof(f284,plain,
! [X2,X0,X1] : mult(rd(X0,X0),X2) = ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,mult(X1,X2)))),
inference(backward_demodulation,[],[f236,f280]) ).
fof(f285,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = mult(rd(X1,X1),X0),
inference(backward_demodulation,[],[f102,f280]) ).
fof(f289,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,mult(rd(X0,X0),rd(X2,X2))),
inference(backward_demodulation,[],[f274,f280]) ).
fof(f292,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(mult(rd(X0,X0),X1),X1)),
inference(superposition,[],[f249,f30]) ).
fof(f293,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(mult(rd(rd(X0,X0),rd(X0,X0)),X1),X1)),
inference(superposition,[],[f249,f171]) ).
fof(f294,plain,
! [X2,X0,X1] : mult(rd(X0,X1),rd(mult(X1,X2),X2)) = rd(mult(rd(mult(X0,X1),X1),X2),X2),
inference(superposition,[],[f249,f4]) ).
fof(f309,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,ld(rd(X0,X0),mult(rd(X0,X0),rd(X1,X1)))),
inference(forward_demodulation,[],[f293,f26]) ).
fof(f310,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,ld(X0,mult(X0,rd(X1,X1)))),
inference(forward_demodulation,[],[f292,f26]) ).
fof(f318,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,mult(rd(X0,X0),rd(X1,X1))),
inference(forward_demodulation,[],[f309,f280]) ).
fof(f319,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = ld(X0,mult(X0,mult(X0,rd(X1,X1)))),
inference(forward_demodulation,[],[f310,f3]) ).
fof(f325,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(mult(X0,X2),X2),
inference(backward_demodulation,[],[f289,f318]) ).
fof(f326,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(forward_demodulation,[],[f319,f154]) ).
fof(f330,plain,
! [X0,X1] : rd(mult(rd(X0,X0),X1),X1) = ld(X0,rd(mult(X0,X1),X1)),
inference(backward_demodulation,[],[f26,f326]) ).
fof(f355,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,rd(mult(rd(X1,X1),X2),X2)),
inference(superposition,[],[f249,f326]) ).
fof(f356,plain,
! [X2,X0,X1] : ld(X0,mult(X0,mult(rd(X1,X1),X2))) = mult(ld(X0,rd(mult(X0,X1),X1)),X2),
inference(superposition,[],[f134,f326]) ).
fof(f359,plain,
! [X2,X0,X1] : rd(mult(ld(X0,mult(X0,X1)),X2),X2) = ld(X0,mult(X0,mult(X1,rd(X2,X2)))),
inference(superposition,[],[f134,f326]) ).
fof(f362,plain,
! [X2,X0,X1] : rd(mult(ld(X0,mult(X0,X1)),X2),X2) = ld(X0,mult(X0,rd(mult(X1,X2),X2))),
inference(forward_demodulation,[],[f359,f326]) ).
fof(f364,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,ld(X1,rd(mult(X1,X2),X2))),
inference(forward_demodulation,[],[f355,f330]) ).
fof(f369,plain,
! [X2,X0,X1] : rd(ld(X0,mult(X0,mult(X1,X2))),X2) = ld(X0,mult(X0,rd(mult(X1,X2),X2))),
inference(forward_demodulation,[],[f362,f134]) ).
fof(f371,plain,
! [X2,X0,X1] : mult(rd(X0,X1),rd(mult(X1,X2),X2)) = mult(X0,ld(X1,rd(mult(X1,X2),X2))),
inference(forward_demodulation,[],[f364,f294]) ).
fof(f378,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,ld(X1,rd(mult(X1,X2),X2))),
inference(backward_demodulation,[],[f294,f371]) ).
fof(f417,plain,
! [X0] : rd(mult(X0,X0),X0) = ld(rd(X0,X0),rd(mult(X0,X0),X0)),
inference(superposition,[],[f280,f4]) ).
fof(f433,plain,
! [X0] : ld(rd(X0,X0),X0) = X0,
inference(forward_demodulation,[],[f417,f2]) ).
fof(f770,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(rd(X0,X0),X1),
inference(superposition,[],[f285,f1]) ).
fof(f771,plain,
! [X2,X0,X1] : mult(rd(X0,X0),X2) = ld(mult(X0,X1),mult(mult(X0,X1),X2)),
inference(superposition,[],[f285,f154]) ).
fof(f786,plain,
! [X0,X1] : ld(X0,X1) = mult(rd(X0,X0),ld(X0,X1)),
inference(superposition,[],[f1,f285]) ).
fof(f827,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = ld(rd(X0,X0),ld(X0,mult(X0,X1))),
inference(backward_demodulation,[],[f280,f770]) ).
fof(f828,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,mult(X1,X2)))),
inference(backward_demodulation,[],[f284,f770]) ).
fof(f830,plain,
! [X0,X1] : ld(X0,rd(mult(X0,X1),X1)) = rd(ld(X0,mult(X0,X1)),X1),
inference(backward_demodulation,[],[f330,f770]) ).
fof(f832,plain,
! [X2,X0,X1] : ld(X0,mult(X0,ld(X1,mult(X1,X2)))) = mult(ld(X0,rd(mult(X0,X1),X1)),X2),
inference(backward_demodulation,[],[f356,f770]) ).
fof(f837,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(mult(X0,X1),mult(mult(X0,X1),X2)),
inference(backward_demodulation,[],[f771,f770]) ).
fof(f840,plain,
! [X0,X1] : ld(X0,X1) = ld(X0,mult(X0,ld(X0,X1))),
inference(backward_demodulation,[],[f786,f770]) ).
fof(f874,plain,
! [X0,X1] : ld(X0,X1) = ld(X0,ld(X0,mult(X0,X1))),
inference(forward_demodulation,[],[f840,f3]) ).
fof(f885,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,rd(ld(X1,mult(X1,X2)),X2)),
inference(backward_demodulation,[],[f378,f830]) ).
fof(f889,plain,
! [X2,X0,X1] : ld(X0,mult(X0,ld(X1,mult(X1,X2)))) = mult(rd(ld(X0,mult(X0,X1)),X1),X2),
inference(backward_demodulation,[],[f832,f830]) ).
fof(f893,plain,
! [X2,X3,X0] : ld(X0,mult(X0,X3)) = ld(X0,mult(X0,mult(X2,ld(ld(X0,mult(X0,X2)),X3)))),
inference(backward_demodulation,[],[f172,f828]) ).
fof(f994,plain,
! [X0,X1] : ld(rd(X0,X1),rd(rd(mult(X0,X1),X1),X1)) = rd(ld(rd(X0,X1),rd(mult(X0,X1),X1)),X1),
inference(superposition,[],[f830,f4]) ).
fof(f997,plain,
! [X2,X0,X1] : rd(ld(mult(X0,X1),mult(mult(X0,X1),X2)),X2) = ld(mult(X0,X1),mult(X0,rd(mult(X1,X2),X2))),
inference(superposition,[],[f830,f249]) ).
fof(f998,plain,
! [X0,X1] : ld(X0,mult(X0,rd(mult(X0,X1),X1))) = mult(X0,rd(ld(X0,mult(X0,X1)),X1)),
inference(superposition,[],[f3,f830]) ).
fof(f999,plain,
! [X0,X1] : rd(ld(X0,mult(X0,mult(X0,X1))),X1) = mult(X0,rd(ld(X0,mult(X0,X1)),X1)),
inference(forward_demodulation,[],[f998,f369]) ).
fof(f1000,plain,
! [X2,X0,X1] : rd(ld(X0,mult(X0,X2)),X2) = ld(mult(X0,X1),mult(X0,rd(mult(X1,X2),X2))),
inference(forward_demodulation,[],[f997,f837]) ).
fof(f1007,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(ld(X0,mult(X0,X1)),X1)),
inference(forward_demodulation,[],[f999,f154]) ).
fof(f1013,plain,
! [X2,X0,X1] : ld(ld(X0,mult(X0,X1)),X2) = ld(ld(X0,mult(X0,X1)),ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,mult(X1,X2))))),
inference(superposition,[],[f874,f134]) ).
fof(f1015,plain,
! [X0,X1] : ld(rd(X0,X0),X1) = ld(rd(X0,X0),ld(rd(X0,X0),ld(X0,mult(X0,X1)))),
inference(superposition,[],[f874,f770]) ).
fof(f1018,plain,
! [X0,X1] : ld(rd(X0,X0),X1) = ld(rd(X0,X0),ld(X0,mult(X0,X1))),
inference(forward_demodulation,[],[f1015,f827]) ).
fof(f1019,plain,
! [X2,X0,X1] : ld(ld(X0,mult(X0,X1)),X2) = ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,X2))),
inference(forward_demodulation,[],[f1013,f828]) ).
fof(f1023,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = ld(rd(X0,X0),X1),
inference(forward_demodulation,[],[f1018,f827]) ).
fof(f1024,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(ld(X0,mult(X0,X1)),mult(X1,X2)),
inference(backward_demodulation,[],[f828,f1019]) ).
fof(f1026,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(rd(X0,X0),X1),
inference(backward_demodulation,[],[f3,f1023]) ).
fof(f1033,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = ld(rd(X0,X0),X1),
inference(backward_demodulation,[],[f770,f1023]) ).
fof(f1036,plain,
! [X0,X1] : ld(X0,rd(mult(X0,X1),X1)) = rd(ld(rd(X0,X0),X1),X1),
inference(backward_demodulation,[],[f830,f1023]) ).
fof(f1038,plain,
! [X2,X0,X1] : ld(mult(X0,X1),mult(mult(X0,X1),X2)) = ld(rd(X0,X0),X2),
inference(backward_demodulation,[],[f837,f1023]) ).
fof(f1041,plain,
! [X0,X1] : ld(X0,X1) = ld(X0,ld(rd(X0,X0),X1)),
inference(backward_demodulation,[],[f874,f1023]) ).
fof(f1043,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,rd(ld(rd(X1,X1),X2),X2)),
inference(backward_demodulation,[],[f885,f1023]) ).
fof(f1047,plain,
! [X2,X0,X1] : ld(X0,mult(X0,ld(X1,mult(X1,X2)))) = mult(rd(ld(rd(X0,X0),X1),X1),X2),
inference(backward_demodulation,[],[f889,f1023]) ).
fof(f1048,plain,
! [X2,X3,X0] : ld(X0,mult(X0,X3)) = ld(X0,mult(X0,mult(X2,ld(ld(rd(X0,X0),X2),X3)))),
inference(backward_demodulation,[],[f893,f1023]) ).
fof(f1052,plain,
! [X2,X0,X1] : ld(mult(X0,X1),mult(X0,rd(mult(X1,X2),X2))) = rd(ld(rd(X0,X0),X2),X2),
inference(backward_demodulation,[],[f1000,f1023]) ).
fof(f1055,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(ld(rd(X0,X0),X1),X1)),
inference(backward_demodulation,[],[f1007,f1023]) ).
fof(f1059,plain,
! [X2,X0] : mult(X0,X2) = ld(rd(X0,X0),mult(X0,X2)),
inference(backward_demodulation,[],[f154,f1023]) ).
fof(f1075,plain,
( mult(x3,x5) != mult(x3,ld(rd(x4,x4),x5))
| spl0_1 ),
inference(backward_demodulation,[],[f12,f1023]) ).
fof(f1076,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(ld(rd(X0,X0),X1),mult(X1,X2)),
inference(forward_demodulation,[],[f1024,f1023]) ).
fof(f1078,definition,
( spl0_2
<=> mult(x3,x5) = mult(x3,ld(rd(x4,x4),x5)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1080,plain,
( mult(x3,x5) != mult(x3,ld(rd(x4,x4),x5))
| spl0_2 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f1081,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f1075,f10,f1078]) ).
fof(f1091,plain,
! [X2,X3,X0] : ld(X0,mult(X0,X3)) = ld(rd(X0,X0),mult(X2,ld(ld(rd(X0,X0),X2),X3))),
inference(forward_demodulation,[],[f1048,f1023]) ).
fof(f1092,plain,
! [X2,X0,X1] : mult(rd(ld(rd(X0,X0),X1),X1),X2) = ld(rd(X0,X0),ld(X1,mult(X1,X2))),
inference(forward_demodulation,[],[f1047,f1023]) ).
fof(f1093,plain,
! [X2,X0,X1] : ld(rd(X0,X0),X2) = ld(rd(mult(X0,X1),mult(X0,X1)),X2),
inference(forward_demodulation,[],[f1038,f1023]) ).
fof(f1100,plain,
! [X2,X0,X1] : ld(rd(X0,X0),X2) = ld(ld(rd(X0,X0),X1),mult(X1,X2)),
inference(forward_demodulation,[],[f1076,f1023]) ).
fof(f1103,plain,
! [X2,X3,X0] : ld(rd(X0,X0),mult(X2,ld(ld(rd(X0,X0),X2),X3))) = ld(rd(X0,X0),X3),
inference(forward_demodulation,[],[f1091,f1023]) ).
fof(f1104,plain,
! [X2,X0,X1] : mult(rd(ld(rd(X0,X0),X1),X1),X2) = ld(rd(X0,X0),ld(rd(X1,X1),X2)),
inference(forward_demodulation,[],[f1092,f1023]) ).
fof(f1134,plain,
! [X0,X1] : ld(rd(X0,X1),rd(rd(mult(X0,X1),X1),X1)) = rd(ld(rd(rd(X0,X1),rd(X0,X1)),X1),X1),
inference(superposition,[],[f1036,f4]) ).
fof(f1141,plain,
! [X0,X1] : rd(ld(rd(X0,X1),rd(mult(X0,X1),X1)),X1) = rd(ld(rd(rd(X0,X1),rd(X0,X1)),X1),X1),
inference(forward_demodulation,[],[f1134,f994]) ).
fof(f1146,plain,
! [X0,X1] : ld(rd(X0,X1),rd(rd(mult(X0,X1),X1),X1)) = rd(ld(rd(rd(X0,X1),rd(X0,X1)),X1),X1),
inference(backward_demodulation,[],[f994,f1141]) ).
fof(f1162,plain,
! [X0,X1] : rd(mult(rd(X0,X0),X1),X1) = ld(rd(X0,X0),rd(X1,X1)),
inference(superposition,[],[f326,f1033]) ).
fof(f1165,plain,
! [X0,X1] : rd(ld(rd(X0,X0),X1),X1) = ld(rd(X0,X0),rd(X1,X1)),
inference(forward_demodulation,[],[f1162,f1033]) ).
fof(f1193,plain,
! [X0,X1] : ld(rd(X0,X1),rd(mult(X0,X1),X1)) = ld(rd(rd(X0,X1),rd(X0,X1)),X1),
inference(superposition,[],[f1023,f4]) ).
fof(f1195,plain,
! [X0,X1] : mult(X0,ld(rd(X0,X0),X1)) = ld(rd(X0,X0),mult(X0,X1)),
inference(superposition,[],[f1026,f1023]) ).
fof(f1198,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(rd(X0,X0),X1)),
inference(forward_demodulation,[],[f1195,f1059]) ).
fof(f1283,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,rd(mult(rd(ld(rd(X0,X0),X1),X1),X2),X2)),
inference(superposition,[],[f249,f1055]) ).
fof(f1296,plain,
! [X2,X0,X1] : rd(mult(rd(mult(X0,X1),X1),X2),X2) = mult(X0,rd(ld(rd(X0,X0),ld(rd(X1,X1),X2)),X2)),
inference(forward_demodulation,[],[f1283,f1104]) ).
fof(f1305,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X1,X1),X2),X2)) = mult(X0,rd(ld(rd(X0,X0),ld(rd(X1,X1),X2)),X2)),
inference(forward_demodulation,[],[f1296,f1043]) ).
fof(f1467,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = rd(rd(mult(X0,X1),X1),rd(X1,X1)),
inference(superposition,[],[f325,f326]) ).
fof(f1468,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = rd(rd(mult(X0,X1),X1),rd(ld(rd(X0,X0),X1),X1)),
inference(superposition,[],[f325,f1055]) ).
fof(f1480,plain,
! [X0,X1] : rd(X0,X1) = rd(mult(rd(X0,X1),X1),X1),
inference(superposition,[],[f2,f325]) ).
fof(f1489,plain,
! [X0,X1] : rd(X0,X1) = rd(rd(mult(X0,X1),X1),X1),
inference(forward_demodulation,[],[f1480,f4]) ).
fof(f1503,plain,
! [X0,X1] : rd(ld(rd(rd(X0,X1),rd(X0,X1)),X1),X1) = ld(rd(X0,X1),rd(X0,X1)),
inference(backward_demodulation,[],[f1146,f1489]) ).
fof(f1508,plain,
! [X0,X1] : rd(rd(X0,X1),rd(X0,X1)) = rd(ld(rd(rd(X0,X1),rd(X0,X1)),X1),X1),
inference(forward_demodulation,[],[f1503,f24]) ).
fof(f1651,plain,
! [X2,X0,X1] : rd(rd(mult(X0,X1),X1),rd(X2,X1)) = rd(X0,rd(X2,X1)),
inference(superposition,[],[f1489,f325]) ).
fof(f1655,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = rd(X0,rd(X1,X1)),
inference(backward_demodulation,[],[f1467,f1651]) ).
fof(f1658,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = rd(X0,rd(ld(rd(X0,X0),X1),X1)),
inference(backward_demodulation,[],[f1468,f1651]) ).
fof(f1663,plain,
! [X0] : rd(X0,rd(ld(rd(X0,X0),X0),X0)) = X0,
inference(backward_demodulation,[],[f2,f1658]) ).
fof(f1665,plain,
! [X2,X0,X1] : rd(mult(mult(X1,X2),X0),X0) = mult(X1,rd(X2,rd(ld(rd(X2,X2),X0),X0))),
inference(backward_demodulation,[],[f249,f1658]) ).
fof(f1669,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = rd(X0,rd(ld(rd(X0,X0),X2),X2)),
inference(backward_demodulation,[],[f325,f1658]) ).
fof(f1670,plain,
! [X0,X1] : mult(X0,rd(X1,X1)) = rd(X0,rd(ld(rd(X0,X0),X1),X1)),
inference(backward_demodulation,[],[f326,f1658]) ).
fof(f1676,plain,
! [X0,X1] : rd(ld(rd(X0,X0),X1),X1) = ld(X0,rd(X0,rd(ld(rd(X0,X0),X1),X1))),
inference(backward_demodulation,[],[f1036,f1658]) ).
fof(f1678,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X1,X1),X2),X2)) = rd(mult(rd(X0,rd(ld(rd(X0,X0),X1),X1)),X2),X2),
inference(backward_demodulation,[],[f1043,f1658]) ).
fof(f1680,plain,
! [X2,X0,X1] : rd(ld(rd(X0,X0),X2),X2) = ld(mult(X0,X1),mult(X0,rd(X1,rd(ld(rd(X1,X1),X2),X2)))),
inference(backward_demodulation,[],[f1052,f1658]) ).
fof(f1689,plain,
! [X0,X1] : ld(rd(rd(X0,X1),rd(X0,X1)),X1) = ld(rd(X0,X1),rd(X0,rd(ld(rd(X0,X0),X1),X1))),
inference(backward_demodulation,[],[f1193,f1658]) ).
fof(f1699,plain,
! [X0,X1] : rd(X0,X1) = rd(rd(X0,rd(ld(rd(X0,X0),X1),X1)),X1),
inference(backward_demodulation,[],[f1489,f1658]) ).
fof(f1715,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = rd(X0,rd(ld(rd(X0,X0),X1),X1)),
inference(forward_demodulation,[],[f1655,f1658]) ).
fof(f1722,plain,
! [X0,X1] : rd(rd(X0,X1),rd(X0,X1)) = rd(ld(rd(X0,X1),rd(X0,rd(ld(rd(X0,X0),X1),X1))),X1),
inference(backward_demodulation,[],[f1508,f1689]) ).
fof(f1735,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X1,X1),X2),X2)) = rd(rd(X0,rd(ld(rd(X0,X0),X1),X1)),rd(ld(rd(rd(X0,rd(ld(rd(X0,X0),X1),X1)),rd(X0,rd(ld(rd(X0,X0),X1),X1))),X2),X2)),
inference(forward_demodulation,[],[f1678,f1658]) ).
fof(f1738,plain,
! [X2,X0,X1] : rd(X0,rd(ld(rd(X0,X0),X2),X2)) = rd(X0,rd(ld(rd(X0,X0),rd(X1,X2)),rd(X1,X2))),
inference(forward_demodulation,[],[f1669,f1658]) ).
fof(f1741,plain,
! [X2,X0,X1] : mult(X1,rd(X2,rd(ld(rd(X2,X2),X0),X0))) = rd(mult(X1,X2),rd(ld(rd(mult(X1,X2),mult(X1,X2)),X0),X0)),
inference(forward_demodulation,[],[f1665,f1658]) ).
fof(f1742,plain,
! [X0] : rd(X0,rd(X0,X0)) = X0,
inference(forward_demodulation,[],[f1663,f433]) ).
fof(f1746,plain,
! [X0,X1] : mult(X0,rd(X1,X1)) = rd(X0,rd(X1,X1)),
inference(backward_demodulation,[],[f1670,f1715]) ).
fof(f1751,plain,
! [X0,X1] : rd(ld(rd(X0,X0),X1),X1) = ld(X0,rd(X0,rd(X1,X1))),
inference(backward_demodulation,[],[f1676,f1715]) ).
fof(f1754,plain,
! [X2,X0,X1] : rd(ld(rd(X0,X0),X2),X2) = ld(mult(X0,X1),mult(X0,rd(X1,rd(X2,X2)))),
inference(backward_demodulation,[],[f1680,f1715]) ).
fof(f1767,plain,
! [X0,X1] : rd(X0,X1) = rd(rd(X0,rd(X1,X1)),X1),
inference(backward_demodulation,[],[f1699,f1715]) ).
fof(f1785,plain,
! [X0,X1] : rd(rd(X0,X1),rd(X0,X1)) = rd(ld(rd(X0,X1),rd(X0,rd(X1,X1))),X1),
inference(forward_demodulation,[],[f1722,f1715]) ).
fof(f1797,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X1,X1),X2),X2)) = rd(rd(X0,rd(ld(rd(X0,X0),X1),X1)),rd(X2,X2)),
inference(forward_demodulation,[],[f1735,f1715]) ).
fof(f1800,plain,
! [X2,X0,X1] : rd(X0,rd(ld(rd(X0,X0),X2),X2)) = rd(X0,rd(rd(X1,X2),rd(X1,X2))),
inference(forward_demodulation,[],[f1738,f1715]) ).
fof(f1803,plain,
! [X2,X0,X1] : mult(X1,rd(X2,rd(ld(rd(X2,X2),X0),X0))) = rd(mult(X1,X2),rd(X0,X0)),
inference(forward_demodulation,[],[f1741,f1715]) ).
fof(f1813,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,X1)) = ld(X0,rd(X0,rd(X1,X1))),
inference(backward_demodulation,[],[f1165,f1751]) ).
fof(f1814,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X0,X0),ld(rd(X1,X1),X2)),X2)) = mult(X0,ld(X1,rd(X1,rd(X2,X2)))),
inference(backward_demodulation,[],[f1305,f1751]) ).
fof(f1819,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = rd(X0,ld(X0,rd(X0,rd(X1,X1)))),
inference(backward_demodulation,[],[f1715,f1751]) ).
fof(f1822,plain,
! [X2,X0,X1] : ld(mult(X0,X1),mult(X0,rd(X1,rd(X2,X2)))) = ld(X0,rd(X0,rd(X2,X2))),
inference(backward_demodulation,[],[f1754,f1751]) ).
fof(f1836,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X1,X1),X2),X2)) = rd(rd(X0,ld(X0,rd(X0,rd(X1,X1)))),rd(X2,X2)),
inference(forward_demodulation,[],[f1797,f1751]) ).
fof(f1838,plain,
! [X2,X0,X1] : rd(X0,rd(rd(X1,X2),rd(X1,X2))) = rd(X0,ld(X0,rd(X0,rd(X2,X2)))),
inference(forward_demodulation,[],[f1800,f1751]) ).
fof(f1841,plain,
! [X2,X0,X1] : rd(mult(X1,X2),rd(X0,X0)) = mult(X1,rd(X2,ld(X2,rd(X2,rd(X0,X0))))),
inference(forward_demodulation,[],[f1803,f1751]) ).
fof(f1853,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X1,X1),X2),X2)) = rd(rd(X0,rd(X1,X1)),rd(X2,X2)),
inference(forward_demodulation,[],[f1836,f1819]) ).
fof(f1855,plain,
! [X2,X0,X1] : rd(X0,rd(rd(X1,X2),rd(X1,X2))) = rd(X0,rd(X2,X2)),
inference(forward_demodulation,[],[f1838,f1819]) ).
fof(f1858,plain,
! [X2,X0,X1] : rd(mult(X1,X2),rd(X0,X0)) = mult(X1,rd(X2,rd(X0,X0))),
inference(forward_demodulation,[],[f1841,f1819]) ).
fof(f1866,plain,
! [X2,X0,X1] : mult(X0,ld(X1,rd(X1,rd(X2,X2)))) = rd(rd(X0,rd(X1,X1)),rd(X2,X2)),
inference(forward_demodulation,[],[f1853,f1751]) ).
fof(f1882,plain,
! [X2,X0,X1] : ld(X0,rd(X0,rd(X2,X2))) = ld(mult(X0,X1),rd(mult(X0,X1),rd(X2,X2))),
inference(backward_demodulation,[],[f1822,f1858]) ).
fof(f1892,plain,
! [X2,X0,X1] : mult(X0,rd(ld(rd(X0,X0),ld(rd(X1,X1),X2)),X2)) = rd(rd(X0,rd(X1,X1)),rd(X2,X2)),
inference(backward_demodulation,[],[f1814,f1866]) ).
fof(f1943,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,X1)) = rd(rd(X0,X0),rd(X1,X1)),
inference(superposition,[],[f1033,f1746]) ).
fof(f1946,plain,
! [X0,X1] : ld(X0,rd(X0,rd(X1,X1))) = rd(rd(X0,X0),rd(X1,X1)),
inference(forward_demodulation,[],[f1943,f1813]) ).
fof(f1952,plain,
! [X0,X1] : rd(ld(rd(X0,X0),X1),X1) = rd(rd(X0,X0),rd(X1,X1)),
inference(backward_demodulation,[],[f1751,f1946]) ).
fof(f1956,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,X1)) = rd(rd(X0,X0),rd(X1,X1)),
inference(backward_demodulation,[],[f1813,f1946]) ).
fof(f1961,plain,
! [X2,X0,X1] : ld(mult(X0,X1),rd(mult(X0,X1),rd(X2,X2))) = rd(rd(X0,X0),rd(X2,X2)),
inference(backward_demodulation,[],[f1882,f1946]) ).
fof(f1965,plain,
! [X2,X0,X1] : rd(rd(X0,X0),rd(X2,X2)) = rd(rd(mult(X0,X1),mult(X0,X1)),rd(X2,X2)),
inference(forward_demodulation,[],[f1961,f1946]) ).
fof(f2049,plain,
! [X0,X1] : mult(X1,X0) = rd(mult(X1,X0),rd(X0,X0)),
inference(superposition,[],[f1858,f1742]) ).
fof(f2114,plain,
! [X2,X0,X1] : ld(X0,ld(rd(X0,X0),X1)) = ld(X0,mult(X2,ld(ld(rd(X0,X0),X2),X1))),
inference(superposition,[],[f1041,f1103]) ).
fof(f2118,plain,
! [X2,X0,X1] : ld(X0,X1) = ld(X0,mult(X2,ld(ld(rd(X0,X0),X2),X1))),
inference(forward_demodulation,[],[f2114,f1041]) ).
fof(f2410,plain,
! [X2,X0,X1] : ld(rd(X2,X2),ld(rd(X0,X0),X1)) = ld(ld(rd(X2,X2),X0),mult(X0,X1)),
inference(superposition,[],[f1100,f1198]) ).
fof(f2428,plain,
! [X2,X0,X1] : ld(rd(X2,X2),ld(rd(X0,X0),X1)) = ld(rd(X2,X2),X1),
inference(forward_demodulation,[],[f2410,f1100]) ).
fof(f2442,plain,
! [X2,X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X2,X2)) = mult(X0,rd(ld(rd(X0,X0),X2),X2)),
inference(backward_demodulation,[],[f1892,f2428]) ).
fof(f2451,plain,
! [X2,X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X2,X2)) = mult(X0,rd(rd(X0,X0),rd(X2,X2))),
inference(forward_demodulation,[],[f2442,f1952]) ).
fof(f2455,plain,
! [X2,X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X2,X2)) = rd(mult(X0,rd(X0,X0)),rd(X2,X2)),
inference(forward_demodulation,[],[f2451,f1858]) ).
fof(f2456,plain,
! [X2,X0,X1] : rd(rd(X0,rd(X1,X1)),rd(X2,X2)) = rd(rd(X0,rd(X0,X0)),rd(X2,X2)),
inference(forward_demodulation,[],[f2455,f1746]) ).
fof(f2457,plain,
! [X2,X0,X1] : rd(X0,rd(X2,X2)) = rd(rd(X0,rd(X1,X1)),rd(X2,X2)),
inference(forward_demodulation,[],[f2456,f1742]) ).
fof(f2472,plain,
! [X2,X0,X1] : rd(rd(X0,rd(X1,X1)),X1) = rd(rd(X0,rd(X2,X2)),X1),
inference(superposition,[],[f1767,f2457]) ).
fof(f2511,plain,
! [X2,X0,X1] : rd(X0,X1) = rd(rd(X0,rd(X2,X2)),X1),
inference(forward_demodulation,[],[f2472,f1767]) ).
fof(f2557,plain,
! [X0,X1] : rd(mult(X0,X1),mult(X0,X1)) = rd(ld(mult(X0,X1),rd(mult(X0,X1),rd(rd(X1,X1),rd(X1,X1)))),rd(X1,X1)),
inference(superposition,[],[f1785,f2049]) ).
fof(f2583,plain,
! [X0,X1] : rd(mult(X0,X1),mult(X0,X1)) = rd(rd(rd(mult(X0,X1),mult(X0,X1)),rd(rd(X1,X1),rd(X1,X1))),rd(X1,X1)),
inference(forward_demodulation,[],[f2557,f1946]) ).
fof(f2597,plain,
! [X0,X1] : rd(mult(X0,X1),mult(X0,X1)) = rd(rd(mult(X0,X1),mult(X0,X1)),rd(X1,X1)),
inference(forward_demodulation,[],[f2583,f2511]) ).
fof(f2609,plain,
! [X0,X1] : rd(mult(X0,X1),mult(X0,X1)) = rd(rd(X0,X0),rd(X1,X1)),
inference(forward_demodulation,[],[f2597,f1965]) ).
fof(f2614,plain,
! [X2,X0,X1] : ld(rd(X0,X0),X2) = ld(rd(rd(X0,X0),rd(X1,X1)),X2),
inference(backward_demodulation,[],[f1093,f2609]) ).
fof(f3095,plain,
! [X0,X1] : rd(rd(X0,X0),rd(rd(X1,X1),rd(X1,X1))) = rd(rd(X0,rd(X1,X1)),rd(X0,rd(X1,X1))),
inference(superposition,[],[f2609,f1746]) ).
fof(f3160,plain,
! [X0,X1] : rd(X0,rd(X0,rd(X1,X1))) = rd(rd(X0,X0),rd(rd(X1,X1),rd(X1,X1))),
inference(forward_demodulation,[],[f3095,f2511]) ).
fof(f3178,plain,
! [X0,X1] : rd(X0,rd(X0,rd(X1,X1))) = rd(rd(X0,X0),rd(X1,X1)),
inference(forward_demodulation,[],[f3160,f1855]) ).
fof(f3208,plain,
! [X0,X1] : ld(rd(X0,X0),rd(X1,X1)) = rd(X0,rd(X0,rd(X1,X1))),
inference(backward_demodulation,[],[f1956,f3178]) ).
fof(f3214,plain,
! [X2,X0,X1] : ld(rd(X0,X0),X2) = ld(rd(X0,rd(X0,rd(X1,X1))),X2),
inference(backward_demodulation,[],[f2614,f3178]) ).
fof(f4694,plain,
! [X2,X0,X1] : ld(X1,X2) = ld(X1,ld(rd(X0,X0),ld(ld(rd(X1,X1),rd(X0,X0)),X2))),
inference(superposition,[],[f2118,f1033]) ).
fof(f4746,plain,
! [X2,X0,X1] : ld(X1,X2) = ld(X1,ld(rd(X0,X0),ld(rd(X1,rd(X1,rd(X0,X0))),X2))),
inference(forward_demodulation,[],[f4694,f3208]) ).
fof(f4787,plain,
! [X2,X0,X1] : ld(X1,X2) = ld(X1,ld(rd(X0,X0),ld(rd(X1,X1),X2))),
inference(forward_demodulation,[],[f4746,f3214]) ).
fof(f4811,plain,
! [X2,X0,X1] : ld(X1,X2) = ld(X1,ld(rd(X0,X0),X2)),
inference(forward_demodulation,[],[f4787,f2428]) ).
fof(f4907,plain,
! [X2,X0,X1] : mult(X0,ld(rd(X0,X0),X1)) = mult(X0,ld(rd(X2,X2),X1)),
inference(superposition,[],[f1198,f4811]) ).
fof(f4912,plain,
! [X2,X0,X1] : mult(X0,X1) = mult(X0,ld(rd(X2,X2),X1)),
inference(forward_demodulation,[],[f4907,f1198]) ).
fof(f4931,plain,
( $false
| spl0_2 ),
inference(backward_subsumption_resolution,[],[f1080,f4912]) ).
fof(f4943,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f4931]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f13]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f4943]) ).
cnf(s4,plain,
spl0_1,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f4972,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP683-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:36:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.60/1.40 % (3188948)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.60/1.40 % (3188954)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=911524442:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.60/1.40 % (3188959)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=249446489:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.60/1.40 % (3188955)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3919201719:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.60/1.40 % (3188958)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1499616929:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.60/1.40 % (3188957)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2634239215:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.60/1.40 % (3188956)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3198669639:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.60/1.40 % (3188953)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3051966481:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.60/1.40 % (3188956)Instruction limit reached!
% 1.60/1.40 % (3188956)------------------------------
% 1.60/1.40 % (3188956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.40 % (3188956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.60/1.40 % (3188956)CaDiCaL version: 2.1.3
% 1.60/1.40 % (3188956)Termination reason: Instruction limit
% 1.60/1.40 % (3188956)Termination phase: Saturation
% 1.60/1.40 % (3188956)Time elapsed: 0.083 s
% 1.60/1.40 % (3188956)Peak memory usage: 89 MB
% 1.60/1.40 % (3188956)Instructions burned: 137 (million)
% 1.60/1.40 % (3188957)Instruction limit reached!
% 1.60/1.40 % (3188957)------------------------------
% 1.60/1.40 % (3188957)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.60/1.40 % (3188957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.60/1.40 % (3188957)CaDiCaL version: 2.1.3
% 1.60/1.40 % (3188957)Termination reason: Instruction limit
% 1.60/1.40 % (3188957)Termination phase: Saturation
% 1.60/1.40 % (3188957)Time elapsed: 0.103 s
% 1.60/1.40 % (3188957)Peak memory usage: 89 MB
% 1.60/1.40 % (3188957)Instructions burned: 181 (million)
% 1.60/1.40 % (3188958)First to succeed.
% 1.60/1.40 % (3188958)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3188948"
% 1.60/1.40 % (3188959)Also succeeded, but the first one will report.
% 1.60/1.40 % (3188967)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2376188041:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 1.60/1.40 % (3188968)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2336230210:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 1.60/1.40 % (3188958)Refutation found. Thanks to Tanya!
% 1.60/1.40 % SZS status Unsatisfiable for theBenchmark
% 1.60/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.60 % (3188958)------------------------------
% 0.16/1.60 % (3188958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.60 % (3188958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.60 % (3188958)CaDiCaL version: 2.1.3
% 0.16/1.60 % (3188958)Termination reason: Refutation
% 0.16/1.60 % (3188958)Time elapsed: 0.159 s
% 0.16/1.60 % (3188958)Peak memory usage: 90 MB
% 0.16/1.60 % (3188958)Instructions burned: 243 (million)
% 0.16/1.60 % (3188958)------------------------------
% 0.16/1.60 % (3188958)------------------------------
% 0.16/1.60 % (3188948)Success in time 0.562 s
% 0.16/1.60 % Vampire exiting
%------------------------------------------------------------------------------