%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP682-11 : 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 : n026.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 2.79s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 68 unt; 1 def)
% Number of atoms : 74 ( 64 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn 146 !; 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,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f10,definition,
( spl0_1
<=> ld(rd(x0,x1),mult(rd(x0,x1),x2)) = ld(x0,mult(x0,x2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f12,plain,
( ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2))
| 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(f26,plain,
! [X0] : ld(X0,X0) = ld(X0,mult(X0,ld(ld(X0,X0),ld(X0,X0)))),
inference(backward_demodulation,[],[f20,f24]) ).
fof(f27,plain,
! [X0,X1] : mult(ld(X0,mult(X0,ld(X1,X1))),X1) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(backward_demodulation,[],[f21,f24]) ).
fof(f28,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(ld(X0,X0),X1),X1),
inference(backward_demodulation,[],[f7,f24]) ).
fof(f29,plain,
! [X0] : rd(mult(X0,X0),X0) = mult(ld(X0,X0),X0),
inference(superposition,[],[f4,f24]) ).
fof(f30,plain,
! [X0] : mult(ld(X0,X0),X0) = X0,
inference(forward_demodulation,[],[f29,f2]) ).
fof(f39,plain,
! [X0] : mult(X0,ld(X0,X0)) = ld(X0,mult(X0,mult(X0,ld(ld(X0,X0),ld(X0,X0))))),
inference(superposition,[],[f3,f26]) ).
fof(f40,plain,
! [X0] : ld(X0,mult(X0,X0)) = ld(X0,mult(X0,mult(X0,ld(ld(X0,X0),ld(X0,X0))))),
inference(forward_demodulation,[],[f39,f3]) ).
fof(f41,plain,
! [X0] : ld(X0,mult(X0,mult(X0,ld(ld(X0,X0),ld(X0,X0))))) = X0,
inference(forward_demodulation,[],[f40,f1]) ).
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(f51,plain,
! [X2,X0,X1] : mult(ld(X1,mult(X1,ld(X0,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(f75,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(f77,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = ld(X1,mult(X1,mult(ld(X0,X0),X0))),
inference(backward_demodulation,[],[f51,f44]) ).
fof(f78,plain,
! [X0,X1] : rd(mult(mult(ld(X0,X0),X1),X1),X1) = ld(X0,mult(X0,mult(ld(X1,X1),X1))),
inference(backward_demodulation,[],[f27,f44]) ).
fof(f79,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = ld(X0,mult(X0,mult(X2,X3))),
inference(backward_demodulation,[],[f5,f44]) ).
fof(f86,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(X0,mult(X0,mult(X2,X3)))),
inference(backward_demodulation,[],[f75,f44]) ).
fof(f106,plain,
! [X2,X0] : mult(X0,X2) = ld(X0,mult(X0,mult(X0,X2))),
inference(backward_demodulation,[],[f58,f79]) ).
fof(f110,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(backward_demodulation,[],[f86,f79]) ).
fof(f124,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = rd(mult(mult(ld(X0,X0),X1),X1),X1),
inference(forward_demodulation,[],[f78,f30]) ).
fof(f125,plain,
! [X2,X0,X1] : ld(ld(X1,X2),mult(ld(X1,X2),X0)) = ld(X1,mult(X1,X0)),
inference(forward_demodulation,[],[f77,f30]) ).
fof(f136,plain,
! [X0] : mult(X0,ld(ld(X0,X0),ld(X0,X0))) = X0,
inference(backward_demodulation,[],[f41,f106]) ).
fof(f168,plain,
! [X2,X0,X1] : mult(X0,rd(mult(ld(ld(X0,X0),ld(X0,X0)),X2),X2)) = rd(mult(X0,rd(X1,X2)),rd(X1,X2)),
inference(superposition,[],[f6,f136]) ).
fof(f170,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(ld(X0,X0),rd(mult(X0,X2),X2)),
inference(superposition,[],[f6,f30]) ).
fof(f172,plain,
! [X2,X0,X1] : mult(X1,rd(mult(X2,X0),X0)) = rd(mult(mult(X1,X2),X0),X0),
inference(superposition,[],[f6,f2]) ).
fof(f191,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X0,X0),rd(mult(X1,X1),X1)),
inference(backward_demodulation,[],[f124,f172]) ).
fof(f201,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(ld(X0,X0),mult(ld(X0,X0),ld(X2,X2)))),
inference(forward_demodulation,[],[f168,f28]) ).
fof(f205,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X0,X0),X1),
inference(forward_demodulation,[],[f191,f2]) ).
fof(f207,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X0,mult(X0,ld(X2,X2)))),
inference(forward_demodulation,[],[f201,f125]) ).
fof(f211,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = ld(X0,mult(X0,rd(mult(X0,X2),X2))),
inference(backward_demodulation,[],[f170,f205]) ).
fof(f212,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = ld(X0,mult(X0,mult(X0,ld(X2,X2)))),
inference(forward_demodulation,[],[f207,f3]) ).
fof(f217,plain,
! [X2,X0,X1] : rd(mult(X0,rd(X1,X2)),rd(X1,X2)) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[],[f212,f106]) ).
fof(f220,plain,
! [X2,X0] : mult(X0,ld(X2,X2)) = ld(X0,mult(X0,rd(mult(X0,X2),X2))),
inference(backward_demodulation,[],[f211,f217]) ).
fof(f336,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = ld(X0,mult(X0,mult(mult(X0,X1),X2))),
inference(superposition,[],[f44,f106]) ).
fof(f345,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,f44]) ).
fof(f350,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,[],[f345,f110]) ).
fof(f362,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(ld(X0,mult(X0,X1)),ld(X0,mult(X0,mult(X1,X2)))),
inference(forward_demodulation,[],[f350,f125]) ).
fof(f372,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,[],[f110,f362]) ).
fof(f382,plain,
! [X2,X0,X1] : mult(ld(X0,X0),rd(mult(X1,X2),X2)) = rd(mult(ld(X0,mult(X0,X1)),X2),X2),
inference(superposition,[],[f172,f205]) ).
fof(f392,plain,
! [X2,X0,X1] : mult(ld(X0,X0),rd(mult(X1,X2),X2)) = rd(ld(X0,mult(X0,mult(X1,X2))),X2),
inference(forward_demodulation,[],[f382,f44]) ).
fof(f397,plain,
! [X2,X0,X1] : ld(X0,mult(X0,rd(mult(X1,X2),X2))) = rd(ld(X0,mult(X0,mult(X1,X2))),X2),
inference(forward_demodulation,[],[f392,f205]) ).
fof(f402,plain,
! [X2,X0] : mult(X0,ld(X2,X2)) = rd(ld(X0,mult(X0,mult(X0,X2))),X2),
inference(backward_demodulation,[],[f220,f397]) ).
fof(f407,plain,
! [X2,X0] : rd(mult(X0,X2),X2) = mult(X0,ld(X2,X2)),
inference(forward_demodulation,[],[f402,f106]) ).
fof(f705,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(X0,mult(X0,mult(mult(X0,X1),ld(mult(X0,X1),X2)))),
inference(superposition,[],[f372,f106]) ).
fof(f736,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = mult(mult(X0,X1),ld(mult(X0,X1),X2)),
inference(forward_demodulation,[],[f705,f336]) ).
fof(f751,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(mult(X0,X1),mult(mult(X0,X1),X2)),
inference(forward_demodulation,[],[f736,f3]) ).
fof(f1267,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(rd(mult(X0,X1),X1),mult(rd(mult(X0,X1),X1),X2)),
inference(superposition,[],[f751,f407]) ).
fof(f1275,plain,
! [X2,X0,X1] : ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(rd(mult(X0,X1),X1),mult(rd(mult(X0,X1),X1),X2)),
inference(superposition,[],[f751,f4]) ).
fof(f1322,plain,
! [X2,X0,X1] : ld(X0,mult(X0,X2)) = ld(rd(X0,X1),mult(rd(X0,X1),X2)),
inference(forward_demodulation,[],[f1267,f1275]) ).
fof(f1329,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f12,f1322]) ).
fof(f1339,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1329]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f13]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1339]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f1348,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP682-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:38:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 2.79/1.31 % (2640649)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.79/1.31 % (2640654)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=1297908597:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.79/1.31 % (2640659)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2669398737:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.79/1.31 % (2640657)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3784576129:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.79/1.31 % (2640655)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=3617754639:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.79/1.31 % (2640656)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=271436603:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.79/1.31 % (2640658)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=932135509:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.79/1.31 % (2640660)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=17651206:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.79/1.31 % (2640659)First to succeed.
% 2.79/1.31 % (2640659)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2640649"
% 2.79/1.31 % (2640657)Instruction limit reached!
% 2.79/1.31 % (2640657)------------------------------
% 2.79/1.31 % (2640657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (2640657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (2640657)CaDiCaL version: 2.1.3
% 2.79/1.31 % (2640657)Termination reason: Instruction limit
% 2.79/1.31 % (2640657)Termination phase: Saturation
% 2.79/1.31 % (2640657)Time elapsed: 0.083 s
% 2.79/1.31 % (2640657)Peak memory usage: 88 MB
% 2.79/1.31 % (2640657)Instructions burned: 136 (million)
% 2.79/1.31 % (2640658)Instruction limit reached!
% 2.79/1.31 % (2640658)------------------------------
% 2.79/1.31 % (2640658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.31 % (2640658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.31 % (2640658)CaDiCaL version: 2.1.3
% 2.79/1.31 % (2640658)Termination reason: Instruction limit
% 2.79/1.31 % (2640658)Termination phase: Saturation
% 2.79/1.31 % (2640658)Time elapsed: 0.103 s
% 2.79/1.31 % (2640658)Peak memory usage: 89 MB
% 2.79/1.31 % (2640658)Instructions burned: 182 (million)
% 2.79/1.31 % (2640668)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2378256915:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 2.79/1.31 % (2640669)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3474219531:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 2.79/1.31 % (2640659)Refutation found. Thanks to Tanya!
% 2.79/1.31 % SZS status Unsatisfiable for theBenchmark
% 2.79/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2640659)------------------------------
% 0.17/1.50 % (2640659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2640659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2640659)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2640659)Termination reason: Refutation
% 0.17/1.50 % (2640659)Time elapsed: 0.064 s
% 0.17/1.50 % (2640659)Peak memory usage: 90 MB
% 0.17/1.50 % (2640659)Instructions burned: 91 (million)
% 0.17/1.50 % (2640659)------------------------------
% 0.17/1.50 % (2640659)------------------------------
% 0.17/1.50 % (2640649)Success in time 0.462 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------