%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 10:16:34 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 32 unt; 3 def)
% Number of atoms : 69 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 18 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = divide(identity,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f6,plain,
( identity != multiply(inverse(a1),a1)
| a2 != multiply(identity,a2)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
( identity != divide(divide(identity,a1),divide(identity,a1))
| a2 != divide(identity,divide(identity,a2))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(definition_unfolding,[],[f6,f2,f3,f2,f2,f2,f2,f2]) ).
fof(f9,definition,
( spl0_1
<=> divide(divide(a3,divide(identity,b3)),divide(identity,c3)) = divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f11,plain,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| spl0_1 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f13,definition,
( spl0_2
<=> a2 = divide(identity,divide(identity,a2)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f15,plain,
( a2 != divide(identity,divide(identity,a2))
| spl0_2 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f17,definition,
( spl0_3
<=> identity = divide(divide(identity,a1),divide(identity,a1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f19,plain,
( identity != divide(divide(identity,a1),divide(identity,a1))
| spl0_3 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f7,f17,f13,f9]) ).
fof(f21,plain,
! [X2,X0,X1] : divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[],[f1,f4]) ).
fof(f24,plain,
! [X0,X1] : divide(X0,divide(identity,divide(divide(identity,X0),divide(identity,X1)))) = X1,
inference(superposition,[],[f21,f4]) ).
fof(f30,plain,
! [X0] : divide(X0,identity) = X0,
inference(superposition,[],[f21,f4]) ).
fof(f36,plain,
! [X0,X1] : divide(X1,divide(divide(identity,X0),divide(divide(identity,X1),identity))) = X0,
inference(superposition,[],[f21,f30]) ).
fof(f37,plain,
! [X0,X1] : divide(X1,divide(divide(identity,X0),divide(identity,X1))) = X0,
inference(forward_demodulation,[],[f36,f30]) ).
fof(f41,plain,
! [X0,X1] : divide(X1,divide(X0,divide(identity,X1))) = divide(divide(identity,X0),divide(identity,identity)),
inference(superposition,[],[f37,f37]) ).
fof(f46,plain,
! [X0] : divide(identity,divide(divide(identity,X0),identity)) = X0,
inference(superposition,[],[f37,f30]) ).
fof(f54,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(forward_demodulation,[],[f46,f30]) ).
fof(f58,plain,
! [X0,X1] : divide(divide(identity,X0),identity) = divide(X1,divide(X0,divide(identity,X1))),
inference(forward_demodulation,[],[f41,f4]) ).
fof(f63,plain,
! [X0,X1] : divide(identity,X0) = divide(X1,divide(X0,divide(identity,X1))),
inference(forward_demodulation,[],[f58,f30]) ).
fof(f306,plain,
! [X0,X1] : divide(divide(divide(identity,divide(identity,X1)),divide(identity,X0)),X0) = X1,
inference(superposition,[],[f37,f24]) ).
fof(f315,plain,
! [X0,X1] : divide(divide(X1,divide(identity,X0)),X0) = X1,
inference(forward_demodulation,[],[f306,f54]) ).
fof(f395,plain,
! [X0,X1] : divide(X1,X0) = divide(identity,divide(X0,divide(identity,divide(identity,X1)))),
inference(superposition,[],[f63,f315]) ).
fof(f396,plain,
! [X0,X1] : divide(X1,X0) = divide(identity,divide(X0,X1)),
inference(forward_demodulation,[],[f395,f54]) ).
fof(f486,plain,
! [X2,X0,X1] : divide(divide(X1,X0),divide(divide(identity,X2),divide(X0,X1))) = X2,
inference(superposition,[],[f37,f396]) ).
fof(f692,plain,
! [X2,X0,X1] : divide(divide(divide(divide(identity,divide(identity,X1)),X2),divide(divide(identity,X0),X2)),X0) = X1,
inference(superposition,[],[f486,f21]) ).
fof(f720,plain,
! [X2,X0,X1] : divide(divide(divide(X1,X2),divide(divide(identity,X0),X2)),X0) = X1,
inference(forward_demodulation,[],[f692,f54]) ).
fof(f955,plain,
! [X2,X0,X1] : divide(X0,X2) = divide(divide(X0,X1),divide(divide(identity,divide(identity,X2)),X1)),
inference(superposition,[],[f315,f720]) ).
fof(f962,plain,
! [X2,X0,X1] : divide(X0,X2) = divide(divide(X0,X1),divide(X2,X1)),
inference(forward_demodulation,[],[f955,f54]) ).
fof(f1010,plain,
! [X2,X0,X1] : divide(X0,divide(X2,X1)) = divide(divide(X0,divide(identity,X1)),X2),
inference(superposition,[],[f962,f315]) ).
fof(f1464,plain,
( divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(a3,divide(divide(identity,c3),b3))
| spl0_1 ),
inference(superposition,[],[f11,f1010]) ).
fof(f1503,plain,
( divide(a3,divide(divide(identity,c3),b3)) != divide(a3,divide(divide(identity,c3),b3))
| spl0_1 ),
inference(forward_demodulation,[],[f1464,f396]) ).
fof(f1504,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f1503]) ).
fof(f1505,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1504]) ).
fof(f1586,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f15,f54]) ).
fof(f1587,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1586]) ).
fof(f1588,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f19,f4]) ).
fof(f1589,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f1588]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f20]) ).
cnf(s314,plain,
spl0_1,
inference(sat_conversion,[],[f1505]) ).
cnf(s335,plain,
spl0_2,
inference(sat_conversion,[],[f1587]) ).
cnf(s336,plain,
spl0_3,
inference(sat_conversion,[],[f1589]) ).
cnf(s337,plain,
$false,
inference(rat,[],[s5,s336,s335,s314]) ).
fof(f1590,plain,
$false,
inference(avatar_sat_refutation,[],[s337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:19:41 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.50 % (237355)Will run a generic schedule for satisfiability detection.
% 0.17/0.50 % (237360)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=433796141_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.50 % TRYING [1]
% 0.17/0.50 % TRYING [2]
% 0.17/0.50 % TRYING [3]
% 0.17/0.50 % TRYING [4]
% 0.17/0.50 % (237361)% WARNING: option uhcvi not known.
% 0.17/0.50 % (237361)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3716376454:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.50 % (237362)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3294557917:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.50 % (237363)dis+10_1_sil=32000:sp=arity:random_seed=2135797854:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.50 % (237364)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=585443022:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.50 % (237365)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=802934866:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.50 % (237366)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1319687805:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.50 % TRYING [5]
% 0.17/0.50 % (237362) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-237355-237362"...
% 0.17/0.50 % (237362)...printing done.
% 0.17/0.50 % (237362)Refutation found. Thanks to Tanya!
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50 % (237362)------------------------------
% 0.17/0.50 % (237362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.50 % (237362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.50 % (237362)CaDiCaL version: 2.1.3
% 0.17/0.50 % (237362)Termination reason: Refutation
% 0.17/0.50 % (237362)Time elapsed: 0.032 s
% 0.17/0.50 % (237362)Peak memory usage: 12 MB
% 0.17/0.50 % (237362)Instructions burned: 56 (million)
% 0.17/0.50 % (237355)Success in time 0.067 s
% 0.17/0.50 % Vampire exiting
%------------------------------------------------------------------------------