%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP096-1 : 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 : n015.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 10:16:38 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 33 unt; 4 def)
% Number of atoms : 89 ( 49 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 : 7 ( 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 : 55 ( 0 sgn 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
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))
| multiply(a4,b4) != multiply(b4,a4) ),
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))
| multiply(a4,b4) != multiply(b4,a4) ),
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))))
| divide(a4,inverse(b4)) != divide(b4,inverse(a4)) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
fof(f7,definition,
( spl0_1
<=> divide(a4,inverse(b4)) = divide(b4,inverse(a4)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f9,plain,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| spl0_1 ),
inference(avatar_component_clause,[],[f7]) ).
fof(f11,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(f13,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| spl0_2 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_3
<=> a2 = divide(divide(inverse(b2),inverse(b2)),inverse(a2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f17,plain,
( a2 != divide(divide(inverse(b2),inverse(b2)),inverse(a2))
| spl0_3 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f19,definition,
( spl0_4
<=> divide(inverse(a1),inverse(a1)) = divide(inverse(b1),inverse(b1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f21,plain,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| spl0_4 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f22,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f5,f19,f15,f11,f7]) ).
fof(f23,plain,
! [X2,X3,X0,X1] : divide(divide(divide(X1,inverse(divide(X0,divide(X1,X2)))),inverse(divide(X3,X0))),X2) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f31,plain,
! [X2,X0] : divide(X0,inverse(divide(X2,X0))) = X2,
inference(superposition,[],[f23,f1]) ).
fof(f36,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(superposition,[],[f31,f31]) ).
fof(f42,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(inverse(X0),inverse(X1)),
inference(superposition,[],[f36,f31]) ).
fof(f48,plain,
! [X0,X1] : inverse(divide(divide(X1,X0),X1)) = X0,
inference(superposition,[],[f42,f36]) ).
fof(f49,plain,
! [X0,X1] : inverse(divide(X1,divide(X0,inverse(X1)))) = X0,
inference(superposition,[],[f42,f31]) ).
fof(f73,plain,
! [X2,X0,X1] : divide(divide(X1,X2),X0) = divide(divide(X1,X0),X2),
inference(superposition,[],[f1,f48]) ).
fof(f86,plain,
! [X0,X1] : divide(divide(X0,X0),inverse(X1)) = X1,
inference(superposition,[],[f1,f49]) ).
fof(f87,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(superposition,[],[f31,f49]) ).
fof(f99,plain,
! [X0,X1] : divide(X1,X1) = inverse(divide(X0,X0)),
inference(superposition,[],[f49,f86]) ).
fof(f105,plain,
! [X2,X0,X1] : divide(divide(divide(X1,X1),inverse(divide(X2,X0))),inverse(X0)) = X2,
inference(superposition,[],[f1,f86]) ).
fof(f106,plain,
! [X2,X0] : divide(divide(X2,X0),inverse(X0)) = X2,
inference(forward_demodulation,[],[f105,f86]) ).
fof(f165,plain,
! [X0,X1] : divide(X1,X1) = divide(X0,X0),
inference(superposition,[],[f99,f99]) ).
fof(f253,plain,
! [X0,X1] : divide(X0,inverse(X1)) = divide(X1,inverse(X0)),
inference(superposition,[],[f106,f87]) ).
fof(f272,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(superposition,[],[f49,f106]) ).
fof(f779,plain,
( divide(a4,inverse(b4)) != divide(a4,inverse(b4))
| spl0_1 ),
inference(superposition,[],[f9,f253]) ).
fof(f801,plain,
! [X0,X1] : inverse(divide(X0,inverse(X1))) = divide(inverse(X0),X1),
inference(superposition,[],[f272,f253]) ).
fof(f819,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f779]) ).
fof(f820,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f819]) ).
fof(f833,plain,
! [X0,X1] : divide(inverse(X1),X0) = divide(inverse(X0),X1),
inference(forward_demodulation,[],[f801,f272]) ).
fof(f961,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3))
| spl0_2 ),
inference(forward_demodulation,[],[f13,f272]) ).
fof(f962,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(c3,inverse(divide(a3,inverse(b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f961,f253]) ).
fof(f963,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(c3,divide(inverse(b3),a3))
| spl0_2 ),
inference(forward_demodulation,[],[f962,f272]) ).
fof(f1534,plain,
! [X2,X0,X1] : divide(X0,X2) = divide(X1,inverse(divide(divide(X0,X1),X2))),
inference(superposition,[],[f31,f73]) ).
fof(f1563,plain,
! [X2,X0,X1] : divide(X0,X2) = divide(X1,divide(X2,divide(X0,X1))),
inference(forward_demodulation,[],[f1534,f272]) ).
fof(f1866,plain,
! [X2,X0,X1] : divide(X1,divide(X0,X2)) = inverse(divide(divide(X0,X1),X2)),
inference(superposition,[],[f48,f1563]) ).
fof(f1886,plain,
! [X2,X0,X1] : divide(X1,divide(X0,X2)) = divide(X2,divide(X0,X1)),
inference(forward_demodulation,[],[f1866,f272]) ).
fof(f2412,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3))
| spl0_2 ),
inference(superposition,[],[f963,f1886]) ).
fof(f2503,plain,
( divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3))
| spl0_2 ),
inference(forward_demodulation,[],[f2412,f833]) ).
fof(f2504,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f2503]) ).
fof(f2505,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2504]) ).
fof(f2628,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f17,f86]) ).
fof(f2629,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f2628]) ).
fof(f2633,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f21,f165]) ).
fof(f2634,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f2633]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s284,plain,
spl0_1,
inference(sat_conversion,[],[f820]) ).
cnf(s688,plain,
spl0_2,
inference(sat_conversion,[],[f2505]) ).
cnf(s782,plain,
spl0_3,
inference(sat_conversion,[],[f2629]) ).
cnf(s783,plain,
spl0_4,
inference(sat_conversion,[],[f2634]) ).
cnf(s784,plain,
$false,
inference(rat,[],[s4,s783,s782,s688,s284]) ).
fof(f2635,plain,
$false,
inference(avatar_sat_refutation,[],[s784]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % 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 09:22:15 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
% 0.16/0.52 % (1389591)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (1389600)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4124614668:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (1389597)% WARNING: option uhcvi not known.
% 0.16/0.52 % (1389597)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2670333500:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (1389596)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=914506557_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (1389598)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4031739410:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (1389599)dis+10_1_sil=32000:sp=arity:random_seed=2613241087:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (1389602)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3097185099:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % (1389601)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2820064420:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % TRYING [4]
% 0.16/0.52 % (1389600)Instruction limit reached!
% 0.16/0.52 % (1389600)------------------------------
% 0.16/0.52 % (1389600)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (1389600)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (1389600)CaDiCaL version: 2.1.3
% 0.16/0.52 % (1389600)Termination reason: Instruction limit
% 0.16/0.52 % (1389600)Termination phase: Saturation
% 0.16/0.52 % (1389600)Time elapsed: 0.039 s
% 0.16/0.52 % (1389600)Peak memory usage: 13 MB
% 0.16/0.52 % (1389600)Instructions burned: 116 (million)
% 0.16/0.52 % (1389610)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=824833282:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % (1389598) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1389591-1389598"...
% 0.16/0.52 % TRYING [4]
% 0.16/0.52 % (1389598)...printing done.
% 0.16/0.52 % (1389598)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (1389598)------------------------------
% 0.16/0.52 % (1389598)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (1389598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (1389598)CaDiCaL version: 2.1.3
% 0.16/0.52 % (1389598)Termination reason: Refutation
% 0.16/0.52 % (1389598)Time elapsed: 0.052 s
% 0.16/0.52 % (1389598)Peak memory usage: 13 MB
% 0.16/0.52 % (1389598)Instructions burned: 91 (million)
% 0.16/0.52 % (1389591)Success in time 0.085 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------