%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP097-1 : 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 : n007.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 0.79s 0.64s
% Output : Refutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 31 unt; 4 def)
% Number of atoms : 87 ( 47 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 : 52 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,inverse(divide(divide(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,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(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(X1,inverse(divide(X0,divide(X1,inverse(divide(divide(X0,X3),divide(X2,X3))))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f29,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X0))) = X1,
inference(superposition,[],[f23,f1]) ).
fof(f33,plain,
! [X0,X1] : divide(X0,inverse(divide(X1,X0))) = X1,
inference(superposition,[],[f23,f29]) ).
fof(f44,plain,
! [X0,X1] : divide(inverse(divide(X1,X1)),inverse(X0)) = X0,
inference(superposition,[],[f33,f29]) ).
fof(f68,plain,
! [X0,X1] : inverse(divide(X0,X0)) = divide(X1,X1),
inference(superposition,[],[f44,f29]) ).
fof(f73,plain,
! [X2,X3,X0,X1] : divide(X0,divide(inverse(divide(X1,X1)),inverse(divide(divide(X0,X2),divide(X3,X2))))) = X3,
inference(superposition,[],[f23,f44]) ).
fof(f82,plain,
! [X2,X0,X1] : divide(inverse(divide(X1,X1)),inverse(divide(divide(X2,inverse(X0)),X0))) = X2,
inference(superposition,[],[f1,f44]) ).
fof(f84,plain,
! [X2,X0] : divide(divide(X2,inverse(X0)),X0) = X2,
inference(forward_demodulation,[],[f82,f44]) ).
fof(f85,plain,
! [X2,X3,X0] : divide(X0,divide(divide(X0,X2),divide(X3,X2))) = X3,
inference(forward_demodulation,[],[f73,f44]) ).
fof(f92,plain,
! [X2,X0] : divide(X0,X0) = divide(X2,X2),
inference(superposition,[],[f68,f68]) ).
fof(f99,plain,
! [X2,X0] : divide(divide(X0,X0),inverse(X2)) = X2,
inference(superposition,[],[f44,f68]) ).
fof(f201,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(superposition,[],[f84,f33]) ).
fof(f211,plain,
! [X0,X1] : divide(X0,inverse(X1)) = divide(X1,inverse(X0)),
inference(superposition,[],[f33,f84]) ).
fof(f229,plain,
! [X0,X1] : divide(X1,X0) = inverse(divide(X0,X1)),
inference(superposition,[],[f201,f33]) ).
fof(f622,plain,
( divide(a4,inverse(b4)) != divide(a4,inverse(b4))
| spl0_1 ),
inference(superposition,[],[f9,f211]) ).
fof(f644,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(divide(X0,inverse(X1))),
inference(superposition,[],[f229,f211]) ).
fof(f657,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f622]) ).
fof(f658,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f657]) ).
fof(f665,plain,
! [X0,X1] : divide(inverse(X1),X0) = divide(inverse(X0),X1),
inference(forward_demodulation,[],[f644,f229]) ).
fof(f739,plain,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3))
| spl0_2 ),
inference(forward_demodulation,[],[f13,f229]) ).
fof(f740,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(c3,inverse(divide(a3,inverse(b3))))
| spl0_2 ),
inference(forward_demodulation,[],[f739,f211]) ).
fof(f741,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(c3,divide(inverse(b3),a3))
| spl0_2 ),
inference(forward_demodulation,[],[f740,f229]) ).
fof(f1253,plain,
! [X2,X0,X1] : divide(X1,X0) = divide(divide(X1,divide(X0,X2)),X2),
inference(superposition,[],[f85,f85]) ).
fof(f1387,plain,
! [X2,X0,X1] : divide(X2,inverse(divide(X0,X1))) = divide(X0,divide(X1,X2)),
inference(superposition,[],[f33,f1253]) ).
fof(f1410,plain,
! [X2,X0,X1] : divide(X0,divide(X1,X2)) = divide(X2,divide(X1,X0)),
inference(forward_demodulation,[],[f1387,f229]) ).
fof(f2033,plain,
( divide(a3,divide(inverse(c3),b3)) != divide(a3,divide(inverse(b3),c3))
| spl0_2 ),
inference(superposition,[],[f741,f1410]) ).
fof(f2126,plain,
( divide(a3,divide(inverse(b3),c3)) != divide(a3,divide(inverse(b3),c3))
| spl0_2 ),
inference(forward_demodulation,[],[f2033,f665]) ).
fof(f2127,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f2126]) ).
fof(f2128,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f2127]) ).
fof(f2257,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f17,f99]) ).
fof(f2258,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f2257]) ).
fof(f2262,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f21,f92]) ).
fof(f2263,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f2262]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f22]) ).
cnf(s218,plain,
spl0_1,
inference(sat_conversion,[],[f658]) ).
cnf(s564,plain,
spl0_2,
inference(sat_conversion,[],[f2128]) ).
cnf(s663,plain,
spl0_3,
inference(sat_conversion,[],[f2258]) ).
cnf(s664,plain,
spl0_4,
inference(sat_conversion,[],[f2263]) ).
cnf(s665,plain,
$false,
inference(rat,[],[s4,s664,s663,s564,s218]) ).
fof(f2264,plain,
$false,
inference(avatar_sat_refutation,[],[s665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.46 % Computer : n007.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 27 09:16:55 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.23/0.51 Running first-order model finding
% 0.23/0.51 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
% 0.79/0.64 % (1149277)Will run a generic schedule for satisfiability detection.
% 0.79/0.64 % (1149283)% WARNING: option uhcvi not known.
% 0.79/0.64 % (1149283)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1352435576:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.79/0.64 % (1149284)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1858118641:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.79/0.64 % (1149282)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2164157777_3000 on theBenchmark for (3000ds/0Mi)
% 0.79/0.64 % (1149288)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1781894480:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.79/0.64 % (1149285)dis+10_1_sil=32000:sp=arity:random_seed=3629937961:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.79/0.64 % TRYING [1]
% 0.79/0.64 % (1149286)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=893719689:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.79/0.64 % TRYING [2]
% 0.79/0.64 % (1149287)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=623643182:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.79/0.64 % TRYING [3]
% 0.79/0.64 % TRYING [4]
% 0.79/0.64 % (1149284) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1149277-1149284"...
% 0.79/0.64 % (1149284)...printing done.
% 0.79/0.64 % (1149284)Refutation found. Thanks to Tanya!
% 0.79/0.64 % SZS status Unsatisfiable for theBenchmark
% 0.79/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 0.79/0.64 % (1149284)------------------------------
% 0.79/0.64 % (1149284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.64 % (1149284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.64 % (1149284)CaDiCaL version: 2.1.3
% 0.79/0.64 % (1149284)Termination reason: Refutation
% 0.79/0.64 % (1149284)Time elapsed: 0.076 s
% 0.79/0.64 % (1149284)Peak memory usage: 13 MB
% 0.79/0.64 % (1149284)Instructions burned: 77 (million)
% 0.79/0.64 % (1149277)Success in time 0.112 s
% 0.79/0.64 % Vampire exiting
%------------------------------------------------------------------------------