%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP584-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 10:18:09 AM UTC 2026
% Result : Unsatisfiable 0.38s 0.49s
% Output : Refutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 81 ( 81 unt; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f6,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f7,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(definition_unfolding,[],[f5,f2,f2]) ).
fof(f8,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,double_divide(double_divide(identity,identity),X0)))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f6]) ).
fof(f9,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(identity,X0),double_divide(X1,identity))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f6]) ).
fof(f11,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),double_divide(identity,identity)) = X0,
inference(superposition,[],[f1,f6]) ).
fof(f12,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)),
inference(superposition,[],[f1,f1]) ).
fof(f13,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,identity)),
inference(superposition,[],[f11,f6]) ).
fof(f16,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(forward_demodulation,[],[f13,f6]) ).
fof(f17,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[],[f16,f6]) ).
fof(f18,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),identity) = X0,
inference(superposition,[],[f11,f17]) ).
fof(f23,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity) = X0,
inference(superposition,[],[f1,f17]) ).
fof(f49,plain,
! [X0] : identity = double_divide(double_divide(double_divide(double_divide(double_divide(identity,X0),identity),identity),X0),double_divide(identity,identity)),
inference(superposition,[],[f9,f11]) ).
fof(f51,plain,
! [X0] : identity = double_divide(double_divide(double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,identity),identity))),identity),X0),double_divide(identity,identity)),
inference(superposition,[],[f9,f8]) ).
fof(f52,plain,
! [X0] : double_divide(identity,X0) = double_divide(double_divide(double_divide(X0,identity),identity),double_divide(identity,identity)),
inference(superposition,[],[f9,f6]) ).
fof(f58,plain,
! [X0] : double_divide(identity,X0) = double_divide(double_divide(double_divide(X0,identity),identity),identity),
inference(forward_demodulation,[],[f52,f17]) ).
fof(f59,plain,
! [X0] : identity = double_divide(double_divide(double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),identity),X0),identity),
inference(forward_demodulation,[],[f51,f17]) ).
fof(f61,plain,
! [X0] : identity = double_divide(double_divide(double_divide(double_divide(double_divide(identity,X0),identity),identity),X0),identity),
inference(forward_demodulation,[],[f49,f17]) ).
fof(f65,plain,
! [X0] : identity = double_divide(double_divide(double_divide(double_divide(identity,double_divide(X0,identity)),identity),X0),identity),
inference(forward_demodulation,[],[f59,f17]) ).
fof(f70,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = double_divide(identity,double_divide(X0,identity)),
inference(superposition,[],[f58,f58]) ).
fof(f103,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))) = double_divide(double_divide(identity,double_divide(identity,X2)),identity),
inference(superposition,[],[f12,f17]) ).
fof(f114,plain,
! [X0,X1] : double_divide(double_divide(identity,X1),double_divide(X0,double_divide(X1,identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)),identity)),double_divide(identity,identity)),
inference(superposition,[],[f11,f12]) ).
fof(f120,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(double_divide(X2,double_divide(identity,identity)),double_divide(X1,X0)))) = X2,
inference(superposition,[],[f1,f12]) ).
fof(f125,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(double_divide(X2,identity),double_divide(X1,X0)))) = X2,
inference(forward_demodulation,[],[f120,f17]) ).
fof(f130,plain,
! [X0,X1] : double_divide(double_divide(identity,X1),double_divide(X0,double_divide(X1,identity))) = double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,X0)),identity),identity)),identity),
inference(forward_demodulation,[],[f114,f17]) ).
fof(f139,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))) = double_divide(identity,double_divide(double_divide(identity,X2),identity)),
inference(forward_demodulation,[],[f103,f70]) ).
fof(f162,plain,
! [X0,X1] : double_divide(double_divide(identity,X1),double_divide(X0,double_divide(X1,identity))) = double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,double_divide(identity,X0)),identity),identity),identity)),
inference(forward_demodulation,[],[f130,f70]) ).
fof(f170,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))) = double_divide(identity,double_divide(identity,double_divide(X2,identity))),
inference(forward_demodulation,[],[f139,f70]) ).
fof(f189,plain,
! [X0,X1] : double_divide(double_divide(identity,X1),double_divide(X0,double_divide(X1,identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,X0)))),
inference(forward_demodulation,[],[f162,f58]) ).
fof(f777,plain,
! [X0] : identity = double_divide(double_divide(X0,double_divide(identity,X0)),identity),
inference(superposition,[],[f65,f18]) ).
fof(f858,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,identity)),identity) = double_divide(X0,double_divide(identity,X0)),
inference(superposition,[],[f23,f777]) ).
fof(f873,plain,
! [X0] : identity = double_divide(X0,double_divide(identity,X0)),
inference(forward_demodulation,[],[f858,f777]) ).
fof(f1115,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)) = double_divide(X0,double_divide(double_divide(identity,identity),identity)),
inference(superposition,[],[f12,f873]) ).
fof(f1116,plain,
! [X0] : double_divide(double_divide(X0,double_divide(double_divide(identity,identity),identity)),double_divide(identity,identity)) = X0,
inference(superposition,[],[f1,f873]) ).
fof(f1163,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,identity)),identity) = X0,
inference(forward_demodulation,[],[f1116,f17]) ).
fof(f1164,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)) = double_divide(X0,double_divide(identity,double_divide(identity,identity))),
inference(forward_demodulation,[],[f1115,f70]) ).
fof(f1181,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = X0,
inference(forward_demodulation,[],[f1163,f17]) ).
fof(f1182,plain,
! [X0] : double_divide(X0,identity) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)),
inference(forward_demodulation,[],[f1164,f6]) ).
fof(f1189,plain,
! [X0] : double_divide(X0,identity) = double_divide(double_divide(identity,double_divide(identity,X0)),identity),
inference(forward_demodulation,[],[f1182,f17]) ).
fof(f1195,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(double_divide(identity,X0),identity)),
inference(forward_demodulation,[],[f1189,f70]) ).
fof(f1196,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(forward_demodulation,[],[f1195,f70]) ).
fof(f1207,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,identity),identity) = double_divide(X1,double_divide(double_divide(identity,X2),double_divide(double_divide(identity,X0),double_divide(X2,X1)))),
inference(superposition,[],[f125,f58]) ).
fof(f1208,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,X0)))) = double_divide(double_divide(double_divide(double_divide(identity,X2),identity),identity),X2),
inference(superposition,[],[f125,f61]) ).
fof(f1230,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(identity,double_divide(X0,double_divide(identity,X0))),double_divide(double_divide(X1,identity),identity))) = X1,
inference(superposition,[],[f125,f777]) ).
fof(f1263,plain,
! [X0,X1] : double_divide(X0,identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,X1),double_divide(double_divide(X0,identity),double_divide(X1,identity))),identity)),
inference(superposition,[],[f70,f125]) ).
fof(f1282,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity))))),identity)),
inference(forward_demodulation,[],[f1263,f189]) ).
fof(f1308,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(identity,double_divide(X0,double_divide(identity,X0))),X1)) = X1,
inference(forward_demodulation,[],[f1230,f1181]) ).
fof(f1328,plain,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,X0)))) = double_divide(double_divide(identity,X2),X2),
inference(forward_demodulation,[],[f1208,f1181]) ).
fof(f1329,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))) = double_divide(double_divide(X0,identity),identity),
inference(forward_demodulation,[],[f1207,f170]) ).
fof(f1346,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))),identity))),
inference(forward_demodulation,[],[f1282,f70]) ).
fof(f1364,plain,
! [X1] : double_divide(identity,double_divide(double_divide(identity,identity),X1)) = X1,
inference(forward_demodulation,[],[f1308,f873]) ).
fof(f1378,plain,
! [X2] : double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(double_divide(identity,X2),X2),
inference(forward_demodulation,[],[f1328,f170]) ).
fof(f1379,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))) = X0,
inference(forward_demodulation,[],[f1329,f1181]) ).
fof(f1392,plain,
! [X0] : double_divide(X0,identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))),identity),
inference(forward_demodulation,[],[f1346,f1196]) ).
fof(f1404,plain,
! [X1] : double_divide(identity,double_divide(identity,X1)) = X1,
inference(forward_demodulation,[],[f1364,f17]) ).
fof(f1413,plain,
! [X2] : double_divide(identity,identity) = double_divide(double_divide(identity,X2),X2),
inference(forward_demodulation,[],[f1378,f1196]) ).
fof(f1414,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(forward_demodulation,[],[f1379,f1196]) ).
fof(f1422,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity)),
inference(forward_demodulation,[],[f1392,f70]) ).
fof(f1434,plain,
! [X2] : identity = double_divide(double_divide(identity,X2),X2),
inference(forward_demodulation,[],[f1413,f17]) ).
fof(f1438,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,X0),
inference(forward_demodulation,[],[f1422,f23]) ).
fof(f1491,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(X1,X0))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f1414]) ).
fof(f1492,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(X1,X0))),identity) = X1,
inference(forward_demodulation,[],[f1491,f17]) ).
fof(f1511,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[],[f1492,f1438]) ).
fof(f1525,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(X1,X0)) = X1,
inference(forward_demodulation,[],[f1511,f1404]) ).
fof(f1532,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[],[f1525,f1404]) ).
fof(f1790,plain,
! [X0,X1] : double_divide(identity,double_divide(X1,X0)) = double_divide(double_divide(X0,double_divide(double_divide(identity,X1),identity)),double_divide(identity,identity)),
inference(superposition,[],[f1,f1434]) ).
fof(f1793,plain,
! [X0,X1] : double_divide(X0,double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(double_divide(X1,identity),identity))) = X1,
inference(superposition,[],[f125,f1434]) ).
fof(f1804,plain,
! [X0,X1] : double_divide(X0,double_divide(double_divide(identity,double_divide(identity,X0)),double_divide(identity,double_divide(X1,identity)))) = X1,
inference(forward_demodulation,[],[f1793,f1438]) ).
fof(f1807,plain,
! [X0,X1] : double_divide(identity,double_divide(X1,X0)) = double_divide(double_divide(X0,double_divide(double_divide(identity,X1),identity)),identity),
inference(forward_demodulation,[],[f1790,f17]) ).
fof(f1826,plain,
! [X0,X1] : double_divide(X0,double_divide(double_divide(identity,double_divide(identity,X0)),X1)) = X1,
inference(forward_demodulation,[],[f1804,f1532]) ).
fof(f1829,plain,
! [X0,X1] : double_divide(identity,double_divide(X1,X0)) = double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),identity))),
inference(forward_demodulation,[],[f1807,f1438]) ).
fof(f1845,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[],[f1826,f1404]) ).
fof(f1847,plain,
! [X0,X1] : double_divide(identity,double_divide(X1,X0)) = double_divide(identity,double_divide(X0,double_divide(identity,double_divide(identity,X1)))),
inference(forward_demodulation,[],[f1829,f1438]) ).
fof(f1859,plain,
! [X0,X1] : double_divide(identity,double_divide(X1,X0)) = double_divide(identity,double_divide(X0,X1)),
inference(forward_demodulation,[],[f1847,f1845]) ).
fof(f2233,plain,
double_divide(double_divide(a,b),identity) != double_divide(identity,double_divide(b,a)),
inference(superposition,[],[f7,f1438]) ).
fof(f2282,plain,
double_divide(double_divide(a,b),identity) != double_divide(identity,double_divide(a,b)),
inference(forward_demodulation,[],[f2233,f1859]) ).
fof(f2330,plain,
$false,
inference(forward_subsumption_resolution,[],[f2282,f1438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP584-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:07:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.38/0.49 % (3769943)Will run a generic schedule for satisfiability detection.
% 0.38/0.49 % (3769952)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2228923311:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.38/0.49 % (3769949)% WARNING: option uhcvi not known.
% 0.38/0.49 % (3769948)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2773535734_3000 on theBenchmark for (3000ds/0Mi)
% 0.38/0.49 % (3769950)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2694886606:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.38/0.49 % (3769949)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=790357825:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.38/0.49 % TRYING [1]
% 0.38/0.49 % TRYING [2]
% 0.38/0.49 % TRYING [3]
% 0.38/0.49 % (3769951)dis+10_1_sil=32000:sp=arity:random_seed=1679113998:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.38/0.49 % (3769953)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=108907947:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.38/0.49 % (3769954)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3733382546:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.38/0.49 % TRYING [4]
% 0.38/0.49 % (3769952) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3769943-3769952"...
% 0.38/0.49 % TRYING [5]
% 0.38/0.49 % (3769952)...printing done.
% 0.38/0.49 % (3769952)Refutation found. Thanks to Tanya!
% 0.38/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.38/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.38/0.49 % (3769952)------------------------------
% 0.38/0.49 % (3769952)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.38/0.49 % (3769952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.38/0.49 % (3769952)CaDiCaL version: 2.1.3
% 0.38/0.49 % (3769952)Termination reason: Refutation
% 0.38/0.49 % (3769952)Time elapsed: 0.033 s
% 0.38/0.49 % (3769952)Peak memory usage: 12 MB
% 0.38/0.49 % (3769952)Instructions burned: 80 (million)
% 0.38/0.49 % (3769943)Success in time 0.056 s
% 0.38/0.49 % Vampire exiting
%------------------------------------------------------------------------------