%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 10:16:39 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 36 unt; 4 def)
% Number of atoms : 92 ( 52 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 30 ~; 29 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(divide(X0,inverse(X1)),X2),divide(X0,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,plain,
! [X0,X1] : divide(X0,inverse(X1)) = multiply(X0,X1),
inference(reorient_equations,[],[f2]) ).
fof(f4,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))
| multiply(a4,b4) != multiply(b4,a4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f5,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))
| multiply(a4,b4) != multiply(b4,a4) ),
inference(reorient_equations,[],[f4]) ).
fof(f6,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))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(definition_unfolding,[],[f5,f3,f3,f3,f3,f3,f3,f3,f3,f3,f3]) ).
fof(f8,definition,
( spl0_1
<=> divide(a4,inverse(b4)) = divide(b4,inverse(a4)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f10,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| spl0_1 ),
inference(avatar_component_clause,[],[f8]) ).
fof(f12,definition,
( spl0_2
<=> divide(divide(a3,inverse(b3)),inverse(c3)) = divide(a3,inverse(divide(b3,inverse(c3)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f14,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| spl0_2 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f16,definition,
( spl0_3
<=> a2 = divide(divide(inverse(b2),inverse(b2)),inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f18,plain,
( a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| spl0_3 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,definition,
( spl0_4
<=> divide(inverse(a1),inverse(a1)) = divide(inverse(b1),inverse(b1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f22,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| spl0_4 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f6,f20,f16,f12,f8]) ).
fof(f24,plain,
! [X2,X0,X1] : divide(X0,divide(divide(X1,inverse(X0)),divide(X1,inverse(X2)))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f25,plain,
! [X2,X3,X0,X1] : divide(divide(divide(divide(divide(X1,inverse(X0)),X2),inverse(X3)),divide(X1,X2)),X0) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f31,plain,
! [X2,X3,X0,X1] : divide(divide(X0,divide(divide(divide(X1,inverse(inverse(X2))),X3),divide(X1,X3))),X0) = X2,
inference(superposition,[],[f25,f25]) ).
fof(f39,plain,
! [X2,X0] : divide(divide(X0,inverse(X2)),X0) = X2,
inference(forward_demodulation,[],[f31,f1]) ).
fof(f41,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),inverse(X0))) = X1,
inference(superposition,[],[f39,f39]) ).
fof(f45,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(superposition,[],[f1,f39]) ).
fof(f53,plain,
! [X0,X1] : divide(divide(X1,X1),inverse(X0)) = X0,
inference(superposition,[],[f45,f39]) ).
fof(f73,plain,
! [X2,X0,X1] : divide(X0,divide(X0,divide(divide(X1,X1),inverse(X2)))) = X2,
inference(superposition,[],[f24,f53]) ).
fof(f76,plain,
! [X2,X0,X1] : divide(divide(divide(divide(X1,X1),inverse(X2)),inverse(X0)),X0) = X2,
inference(superposition,[],[f1,f53]) ).
fof(f79,plain,
! [X2,X0] : divide(divide(X2,inverse(X0)),X0) = X2,
inference(forward_demodulation,[],[f76,f53]) ).
fof(f81,plain,
! [X2,X0] : divide(X0,divide(X0,X2)) = X2,
inference(forward_demodulation,[],[f73,f53]) ).
fof(f88,plain,
! [X0,X1] : divide(X1,X1) = divide(X0,X0),
inference(superposition,[],[f81,f45]) ).
fof(f147,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f79,f53]) ).
fof(f170,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X0),X1),
inference(superposition,[],[f39,f147]) ).
fof(f291,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(superposition,[],[f170,f81]) ).
fof(f482,plain,
! [X0,X1] : divide(inverse(X0),inverse(X1)) = divide(X1,X0),
inference(superposition,[],[f24,f41]) ).
fof(f504,plain,
! [X0,X1] : divide(X0,inverse(X1)) = divide(X1,inverse(X0)),
inference(superposition,[],[f482,f147]) ).
fof(f507,plain,
! [X0,X1] : divide(inverse(X1),X0) = divide(inverse(X0),X1),
inference(superposition,[],[f482,f147]) ).
fof(f519,plain,
! [X2,X0,X1] : divide(X0,divide(divide(X0,X1),divide(inverse(X1),inverse(X2)))) = X2,
inference(superposition,[],[f24,f482]) ).
fof(f541,plain,
! [X2,X0,X1] : divide(X0,divide(divide(X0,X1),divide(X2,X1))) = X2,
inference(forward_demodulation,[],[f519,f482]) ).
fof(f708,plain,
( divide(a4,inverse(b4)) != divide(a4,inverse(b4))
| spl0_1 ),
inference(superposition,[],[f10,f504]) ).
fof(f769,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f708]) ).
fof(f770,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f849,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3))
| spl0_2 ),
inference(forward_demodulation,[],[f14,f291]) ).
fof(f850,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(c3,inverse(divide(a3,inverse(b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f849,f504]) ).
fof(f851,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(c3,divide(inverse(b3),a3))
| spl0_2 ),
inference(forward_demodulation,[],[f850,f291]) ).
fof(f997,plain,
! [X2,X0,X1] : divide(X1,divide(X0,divide(X2,divide(X1,X0)))) = X2,
inference(superposition,[],[f541,f81]) ).
fof(f1133,plain,
! [X2,X0,X1] : divide(X0,inverse(divide(X1,X2))) = divide(X1,divide(X2,X0)),
inference(superposition,[],[f997,f79]) ).
fof(f1165,plain,
! [X2,X0,X1] : divide(X0,divide(X2,X1)) = divide(X1,divide(X2,X0)),
inference(forward_demodulation,[],[f1133,f291]) ).
fof(f1955,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3))
| spl0_2 ),
inference(superposition,[],[f851,f1165]) ).
fof(f2113,plain,
( divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3))
| spl0_2 ),
inference(forward_demodulation,[],[f1955,f507]) ).
fof(f2114,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f2113]) ).
fof(f2115,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2114]) ).
fof(f2196,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f18,f53]) ).
fof(f2197,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f2196]) ).
fof(f2201,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f22,f88]) ).
fof(f2202,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f2201]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f23]) ).
cnf(s247,plain,
spl0_1,
inference(sat_conversion,[],[f770]) ).
cnf(s656,plain,
spl0_2,
inference(sat_conversion,[],[f2115]) ).
cnf(s750,plain,
spl0_3,
inference(sat_conversion,[],[f2197]) ).
cnf(s751,plain,
spl0_4,
inference(sat_conversion,[],[f2202]) ).
cnf(s752,plain,
$false,
inference(rat,[],[s4,s751,s750,s656,s247]) ).
fof(f2203,plain,
$false,
inference(avatar_sat_refutation,[],[s752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n005.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 09:18:47 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
% 0.17/0.49 % (3726113)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (3726125)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3803295283:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (3726124)% WARNING: option uhcvi not known.
% 0.17/0.49 % (3726124)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=322155683:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (3726126)dis+10_1_sil=32000:sp=arity:random_seed=393844299:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (3726122)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2093499601_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (3726128)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4235347704:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (3726127)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=281646346:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (3726129)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2150381893:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (3726125) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3726113-3726125"...
% 0.17/0.49 % (3726125)...printing done.
% 0.17/0.49 % (3726125)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (3726125)------------------------------
% 0.17/0.49 % (3726125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (3726125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (3726125)CaDiCaL version: 2.1.3
% 0.17/0.49 % (3726125)Termination reason: Refutation
% 0.17/0.49 % (3726125)Time elapsed: 0.027 s
% 0.17/0.49 % (3726125)Peak memory usage: 13 MB
% 0.17/0.49 % (3726125)Instructions burned: 82 (million)
% 0.17/0.49 % (3726113)Success in time 0.055 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------