%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP070-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 10:16:35 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 27 unt; 3 def)
% Number of atoms : 64 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 20 ~; 18 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : divide(divide(X0,X0),divide(X1,divide(divide(X2,divide(X3,X1)),inverse(X3)))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2]) ).
fof(f7,definition,
( spl0_1
<=> divide(divide(a3,inverse(b3)),inverse(c3)) = divide(a3,inverse(divide(b3,inverse(c3)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f11,definition,
( spl0_2
<=> a2 = divide(divide(inverse(b2),inverse(b2)),inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f13,plain,
( a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_3
<=> divide(inverse(a1),inverse(a1)) = divide(inverse(b1),inverse(b1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f5,f15,f11,f7]) ).
fof(f20,plain,
! [X2,X3,X0,X1,X4] : divide(X4,X4) = divide(divide(X1,X1),divide(divide(divide(X0,divide(X2,X3)),inverse(X2)),divide(X0,inverse(X3)))),
inference(superposition,[],[f1,f1]) ).
fof(f30,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(superposition,[],[f20,f20]) ).
fof(f46,plain,
! [X2,X3,X0,X1] : divide(divide(X1,X1),divide(X2,divide(divide(X3,divide(X0,X0)),inverse(X2)))) = X3,
inference(superposition,[],[f1,f30]) ).
fof(f48,plain,
! [X2,X3,X0,X1] : divide(X3,X2) = divide(divide(X1,X1),divide(X2,divide(divide(X0,X0),inverse(X3)))),
inference(superposition,[],[f1,f30]) ).
fof(f84,plain,
! [X2,X0,X1] : divide(X0,X0) = divide(X1,divide(divide(X2,X2),inverse(X1))),
inference(superposition,[],[f48,f30]) ).
fof(f134,plain,
! [X2,X3,X0,X1] : divide(divide(X1,X1),divide(inverse(X2),divide(divide(X0,X0),inverse(divide(X3,X3))))) = X2,
inference(superposition,[],[f1,f84]) ).
fof(f137,plain,
! [X2,X3] : divide(divide(X3,X3),inverse(X2)) = X2,
inference(forward_demodulation,[],[f134,f48]) ).
fof(f145,plain,
! [X2,X0,X1] : divide(divide(X1,X1),divide(X2,X0)) = divide(X0,X2),
inference(superposition,[],[f1,f137]) ).
fof(f255,plain,
! [X2,X3,X0] : divide(divide(divide(X0,divide(X3,X2)),inverse(X3)),X2) = X0,
inference(superposition,[],[f145,f1]) ).
fof(f276,plain,
! [X2,X3,X0,X1] : divide(X0,divide(X2,X2)) = divide(divide(X3,X3),divide(inverse(X0),divide(X1,X1))),
inference(superposition,[],[f48,f145]) ).
fof(f297,plain,
! [X2,X0,X1] : divide(X0,divide(X2,X2)) = divide(divide(X1,X1),inverse(X0)),
inference(forward_demodulation,[],[f276,f145]) ).
fof(f315,plain,
! [X2,X0] : divide(X0,divide(X2,X2)) = X0,
inference(forward_demodulation,[],[f297,f137]) ).
fof(f338,plain,
! [X2,X0,X1] : divide(divide(X1,X1),divide(X2,divide(X0,inverse(X2)))) = X0,
inference(superposition,[],[f46,f315]) ).
fof(f365,plain,
! [X2,X0] : divide(divide(X0,inverse(X2)),X2) = X0,
inference(forward_demodulation,[],[f338,f145]) ).
fof(f384,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(superposition,[],[f365,f145]) ).
fof(f1133,plain,
! [X2,X0,X1] : divide(X0,inverse(divide(X1,X2))) = divide(divide(X0,inverse(X1)),X2),
inference(superposition,[],[f255,f365]) ).
fof(f1191,plain,
! [X2,X0,X1] : divide(X0,divide(X2,X1)) = divide(divide(X0,inverse(X1)),X2),
inference(forward_demodulation,[],[f1133,f384]) ).
fof(f1347,plain,
( divide(a3,inverse(divide(b3,inverse(c3)))) != divide(a3,divide(inverse(c3),b3))
| spl0_1 ),
inference(superposition,[],[f9,f1191]) ).
fof(f1361,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(c3),b3))
| spl0_1 ),
inference(forward_demodulation,[],[f1347,f384]) ).
fof(f1362,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f1361]) ).
fof(f1363,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1362]) ).
fof(f1500,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f13,f137]) ).
fof(f1501,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1500]) ).
fof(f1502,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f17,f30]) ).
fof(f1503,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f1502]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f18]) ).
cnf(s374,plain,
spl0_1,
inference(sat_conversion,[],[f1363]) ).
cnf(s397,plain,
spl0_2,
inference(sat_conversion,[],[f1501]) ).
cnf(s398,plain,
spl0_3,
inference(sat_conversion,[],[f1503]) ).
cnf(s399,plain,
$false,
inference(rat,[],[s4,s398,s397,s374]) ).
fof(f1504,plain,
$false,
inference(avatar_sat_refutation,[],[s399]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP070-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n020.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:18:49 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.15/0.50 % (3122571)Will run a generic schedule for satisfiability detection.
% 0.15/0.50 % (3122581)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3935734829:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.50 % (3122577)% WARNING: option uhcvi not known.
% 0.15/0.50 % (3122578)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2760641037:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.50 % (3122576)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4075676242_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.50 % (3122577)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1654368674:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.50 % (3122579)dis+10_1_sil=32000:sp=arity:random_seed=1853246419:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.50 % (3122580)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4129430754:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.50 % (3122582)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3947762037:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.50 % TRYING [1]
% 0.15/0.50 % TRYING [2]
% 0.15/0.50 % TRYING [3]
% 0.15/0.50 % TRYING [4]
% 0.15/0.50 % (3122578) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3122571-3122578"...
% 0.15/0.50 % (3122578)...printing done.
% 0.15/0.50 % (3122581)Instruction limit reached!
% 0.15/0.50 % (3122581)------------------------------
% 0.15/0.50 % (3122581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (3122581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (3122581)CaDiCaL version: 2.1.3
% 0.15/0.50 % (3122581)Termination reason: Instruction limit
% 0.15/0.50 % (3122581)Termination phase: Saturation
% 0.15/0.50 % (3122581)Time elapsed: 0.041 s
% 0.15/0.50 % (3122581)Peak memory usage: 13 MB
% 0.15/0.50 % (3122581)Instructions burned: 133 (million)
% 0.15/0.50 % (3122578)Refutation found. Thanks to Tanya!
% 0.15/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.50 % (3122578)------------------------------
% 0.15/0.50 % (3122578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.50 % (3122578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.50 % (3122578)CaDiCaL version: 2.1.3
% 0.15/0.50 % (3122578)Termination reason: Refutation
% 0.15/0.50 % (3122578)Time elapsed: 0.032 s
% 0.15/0.50 % (3122578)Peak memory usage: 12 MB
% 0.15/0.50 % (3122578)Instructions burned: 54 (million)
% 0.15/0.50 % (3122571)Success in time 0.073 s
% 0.15/0.50 % Vampire exiting
%------------------------------------------------------------------------------