%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP572-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:14:53 AM UTC 2026
% Result : Unsatisfiable 2.80s 1.25s
% Output : Refutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 77 ( 37 unt; 3 def)
% Number of atoms : 132 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 109 ( 54 ~; 52 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 103 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f7,definition,
( spl0_1
<=> multiply(a,b) = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( multiply(a,b) != multiply(b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f10,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f5,f7]) ).
fof(f11,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),double_divide(identity,identity)) = X1,
inference(backward_demodulation,[],[f1,f3]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f13,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f11,f3]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f12,f3]) ).
fof(f21,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(superposition,[],[f13,f3]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[],[f13,f4]) ).
fof(f24,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(X2,double_divide(double_divide(X3,double_divide(X2,double_divide(X1,X0))),multiply(X0,X1))),inverse(identity)) = X3,
inference(superposition,[],[f13,f12]) ).
fof(f29,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f22,f3]) ).
fof(f81,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(superposition,[],[f29,f4]) ).
fof(f87,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[],[f81,f3]) ).
fof(f88,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),inverse(identity)),
inference(superposition,[],[f87,f12]) ).
fof(f92,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,X0),inverse(inverse(identity)))),inverse(identity)) = X1,
inference(superposition,[],[f13,f87]) ).
fof(f118,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(superposition,[],[f21,f21]) ).
fof(f119,plain,
! [X0,X1] : double_divide(X1,double_divide(inverse(X0),inverse(inverse(X1)))) = double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),
inference(superposition,[],[f21,f29]) ).
fof(f120,plain,
! [X0] : inverse(X0) = double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),
inference(superposition,[],[f21,f87]) ).
fof(f126,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,double_divide(inverse(X0),inverse(inverse(X1)))),
inference(forward_demodulation,[],[f119,f120]) ).
fof(f127,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(forward_demodulation,[],[f118,f120]) ).
fof(f293,plain,
! [X2,X0,X1] : double_divide(double_divide(X1,double_divide(double_divide(X2,inverse(X0)),multiply(inverse(inverse(X1)),inverse(X0)))),inverse(identity)) = X2,
inference(superposition,[],[f24,f126]) ).
fof(f297,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(double_divide(inverse(X0),inverse(inverse(X1))),X1),
inference(superposition,[],[f12,f126]) ).
fof(f313,plain,
! [X0] : inverse(inverse(X0)) = double_divide(identity,double_divide(X0,inverse(identity))),
inference(superposition,[],[f127,f87]) ).
fof(f334,plain,
double_divide(identity,identity) = inverse(inverse(identity)),
inference(superposition,[],[f313,f4]) ).
fof(f337,plain,
! [X0] : double_divide(identity,X0) = inverse(inverse(inverse(X0))),
inference(superposition,[],[f313,f87]) ).
fof(f357,plain,
inverse(identity) = inverse(inverse(identity)),
inference(forward_demodulation,[],[f334,f3]) ).
fof(f366,definition,
( spl0_2
<=> inverse(identity) = inverse(inverse(identity)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f368,plain,
( inverse(identity) = inverse(inverse(identity))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f369,plain,
spl0_2,
inference(avatar_split_clause,[],[f357,f366]) ).
fof(f374,plain,
( ! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,X0),inverse(identity))),inverse(identity)) = X1
| ~ spl0_2 ),
inference(backward_demodulation,[],[f92,f368]) ).
fof(f389,plain,
identity = inverse(inverse(inverse(inverse(identity)))),
inference(superposition,[],[f4,f337]) ).
fof(f392,plain,
( identity = inverse(inverse(inverse(identity)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f389,f368]) ).
fof(f408,plain,
( identity = inverse(inverse(identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f392,f368]) ).
fof(f418,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f408,f368]) ).
fof(f427,definition,
( spl0_3
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f429,plain,
( identity = inverse(identity)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f430,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f418,f366,f427]) ).
fof(f444,plain,
( ! [X0] : double_divide(inverse(X0),identity) = X0
| ~ spl0_3 ),
inference(backward_demodulation,[],[f87,f429]) ).
fof(f445,plain,
( ! [X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),identity)
| ~ spl0_3 ),
inference(backward_demodulation,[],[f88,f429]) ).
fof(f451,plain,
( ! [X2,X0,X1] : double_divide(double_divide(X1,double_divide(double_divide(X2,inverse(X0)),multiply(inverse(inverse(X1)),inverse(X0)))),identity) = X2
| ~ spl0_3 ),
inference(backward_demodulation,[],[f293,f429]) ).
fof(f458,plain,
( ! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,X0),identity)),identity) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[],[f374,f429]) ).
fof(f461,plain,
( ! [X0,X1] : inverse(double_divide(inverse(X0),double_divide(double_divide(X1,X0),identity))) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f458,f3]) ).
fof(f467,plain,
( ! [X2,X0,X1] : inverse(double_divide(X1,double_divide(double_divide(X2,inverse(X0)),multiply(inverse(inverse(X1)),inverse(X0))))) = X2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f451,f3]) ).
fof(f473,plain,
( ! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1))
| ~ spl0_3 ),
inference(forward_demodulation,[],[f445,f3]) ).
fof(f474,plain,
( ! [X0] : inverse(inverse(X0)) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f444,f3]) ).
fof(f477,plain,
( ! [X0,X1] : multiply(double_divide(double_divide(X1,X0),identity),inverse(X0)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f461,f12]) ).
fof(f481,plain,
( ! [X2,X0,X1] : multiply(double_divide(double_divide(X2,inverse(X0)),multiply(inverse(inverse(X1)),inverse(X0))),X1) = X2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f467,f12]) ).
fof(f502,plain,
( ! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(multiply(inverse(inverse(X1)),inverse(X0))),X1)
| ~ spl0_3 ),
inference(backward_demodulation,[],[f297,f473]) ).
fof(f504,plain,
( ! [X0] : multiply(identity,X0) = X0
| ~ spl0_3 ),
inference(backward_demodulation,[],[f14,f474]) ).
fof(f508,plain,
( ! [X0,X1] : multiply(inverse(multiply(identity,double_divide(X1,X0))),inverse(X0)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f477,f473]) ).
fof(f512,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(multiply(inverse(inverse(X1)),inverse(X0)),double_divide(X2,inverse(X0)))),X1) = X2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f481,f473]) ).
fof(f517,plain,
( ! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(multiply(X1,inverse(X0))),X1)
| ~ spl0_3 ),
inference(forward_demodulation,[],[f502,f474]) ).
fof(f530,plain,
( ! [X0,X1] : multiply(inverse(double_divide(X1,X0)),inverse(X0)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f508,f504]) ).
fof(f533,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(multiply(inverse(inverse(X1)),inverse(X0)),inverse(multiply(inverse(X0),X2)))),X1) = X2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f512,f473]) ).
fof(f536,plain,
( ! [X0,X1] : multiply(inverse(multiply(X1,inverse(X0))),X1) = X0
| ~ spl0_3 ),
inference(forward_demodulation,[],[f517,f474]) ).
fof(f546,plain,
( ! [X0,X1] : multiply(inverse(inverse(multiply(X0,X1))),inverse(X0)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f530,f473]) ).
fof(f548,plain,
( ! [X2,X0,X1] : multiply(inverse(multiply(multiply(X1,inverse(X0)),inverse(multiply(inverse(X0),X2)))),X1) = X2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f533,f474]) ).
fof(f556,plain,
( ! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f546,f474]) ).
fof(f912,plain,
( ! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f536,f556]) ).
fof(f1172,plain,
( ! [X0,X1] : multiply(inverse(inverse(X0)),multiply(inverse(X0),X1)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f548,f556]) ).
fof(f1203,plain,
( ! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f1172,f474]) ).
fof(f1261,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(X1,X0)
| ~ spl0_2
| ~ spl0_3 ),
inference(superposition,[],[f1203,f912]) ).
fof(f1292,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_subsumption_resolution,[],[f9,f1261]) ).
fof(f1293,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f1292]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f10]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f369]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f430]) ).
cnf(s6,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f1293]) ).
cnf(s7,plain,
spl0_3,
inference(rat,[],[s3,s2]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s6,s2,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
fof(f1297,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP572-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.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 10:07:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 2.80/1.25 % (3279645)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.80/1.25 % (3279756)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=442325036:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.80/1.25 % (3279756)First to succeed.
% 2.80/1.25 % (3279756)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3279645"
% 2.80/1.25 % (3279754)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1371120878:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.80/1.25 % (3279753)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2926127893:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.80/1.25 % (3279755)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3334417429:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.80/1.25 % (3279752)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=2544959082:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.80/1.25 % (3279751)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=280940048:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.80/1.25 % (3279754)Also succeeded, but the first one will report.
% 2.80/1.25 % (3279757)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1675835133:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.80/1.25 % (3279755)Also succeeded, but the first one will report.
% 2.80/1.25 % (3279757)Also succeeded, but the first one will report.
% 2.80/1.25 % (3279756)Refutation found. Thanks to Tanya!
% 2.80/1.25 % SZS status Unsatisfiable for theBenchmark
% 2.80/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.25/1.45 % (3279756)------------------------------
% 3.25/1.45 % (3279756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.25/1.45 % (3279756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.25/1.45 % (3279756)CaDiCaL version: 2.1.3
% 3.25/1.45 % (3279756)Termination reason: Refutation
% 3.25/1.45 % (3279756)Time elapsed: 0.019 s
% 3.25/1.45 % (3279756)Peak memory usage: 89 MB
% 3.25/1.45 % (3279756)Instructions burned: 51 (million)
% 3.25/1.45 % (3279756)------------------------------
% 3.25/1.45 % (3279756)------------------------------
% 3.25/1.45 % (3279645)Success in time 0.382 s
% 3.25/1.45 % Vampire exiting
%------------------------------------------------------------------------------