%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP086-1 : 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 10:16:37 AM UTC 2026
% Result : Unsatisfiable 1.29s 0.64s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 32 unt; 4 def)
% Number of atoms : 88 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 28 ~; 28 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,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(f3,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,[],[f2]) ).
fof(f5,definition,
( spl0_1
<=> multiply(a4,b4) = multiply(b4,a4) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(a4,b4) != multiply(b4,a4)
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f9,definition,
( spl0_2
<=> multiply(multiply(a3,b3),c3) = multiply(a3,multiply(b3,c3)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f11,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(avatar_component_clause,[],[f9]) ).
fof(f13,definition,
( spl0_3
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f15,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_3 ),
inference(avatar_component_clause,[],[f13]) ).
fof(f17,definition,
( spl0_4
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f19,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| spl0_4 ),
inference(avatar_component_clause,[],[f17]) ).
fof(f20,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f3,f17,f13,f9,f5]) ).
fof(f21,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(multiply(X0,X3),inverse(multiply(X2,X3))))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f27,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(superposition,[],[f21,f1]) ).
fof(f30,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[],[f21,f27]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(X0,inverse(multiply(X3,multiply(X2,inverse(X2))))))))) = X3,
inference(superposition,[],[f21,f27]) ).
fof(f37,plain,
! [X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(X0,inverse(X3)))))) = X3,
inference(forward_demodulation,[],[f32,f27]) ).
fof(f39,plain,
! [X2,X0,X1] : multiply(multiply(X2,X1),multiply(X0,inverse(multiply(X0,X1)))) = X2,
inference(superposition,[],[f21,f30]) ).
fof(f54,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(multiply(X0,X1),multiply(X2,inverse(X0))),
inference(superposition,[],[f21,f39]) ).
fof(f75,plain,
! [X2,X0,X1] : multiply(X1,X2) = multiply(X1,multiply(multiply(X0,X2),inverse(X0))),
inference(superposition,[],[f37,f1]) ).
fof(f95,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[],[f75,f54]) ).
fof(f141,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(X2,multiply(multiply(X0,inverse(X0)),X1)),
inference(superposition,[],[f75,f95]) ).
fof(f191,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X1,inverse(X0)))) = X0,
inference(superposition,[],[f141,f1]) ).
fof(f195,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[],[f141,f30]) ).
fof(f258,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(superposition,[],[f1,f191]) ).
fof(f260,plain,
! [X0,X1] : multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(forward_demodulation,[],[f258,f95]) ).
fof(f281,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(superposition,[],[f191,f260]) ).
fof(f284,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f30,f260]) ).
fof(f306,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[],[f284,f260]) ).
fof(f315,plain,
( multiply(a4,b4) != multiply(a4,b4)
| spl0_1 ),
inference(superposition,[],[f7,f284]) ).
fof(f377,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f315]) ).
fof(f378,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f387,plain,
( multiply(a3,multiply(b3,c3)) != multiply(c3,multiply(a3,b3))
| spl0_2 ),
inference(forward_demodulation,[],[f11,f284]) ).
fof(f388,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f281,f284]) ).
fof(f409,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f388,f30]) ).
fof(f580,plain,
! [X2,X0,X1] : multiply(X1,multiply(X0,X2)) = multiply(X0,multiply(X1,inverse(inverse(X2)))),
inference(superposition,[],[f54,f306]) ).
fof(f587,plain,
! [X2,X0,X1] : multiply(X1,multiply(X0,X2)) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[],[f580,f409]) ).
fof(f3241,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(c3,b3))
| spl0_2 ),
inference(superposition,[],[f387,f587]) ).
fof(f3330,plain,
( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| spl0_2 ),
inference(forward_demodulation,[],[f3241,f284]) ).
fof(f3331,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f3330]) ).
fof(f3332,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f3331]) ).
fof(f3528,plain,
( a2 != multiply(a2,multiply(inverse(b2),b2))
| spl0_3 ),
inference(forward_demodulation,[],[f15,f284]) ).
fof(f3529,plain,
( a2 != multiply(a2,multiply(b2,inverse(b2)))
| spl0_3 ),
inference(forward_demodulation,[],[f3528,f284]) ).
fof(f3530,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f3529,f27]) ).
fof(f3531,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f3530]) ).
fof(f3533,plain,
( multiply(inverse(a1),a1) != multiply(b1,inverse(b1))
| spl0_4 ),
inference(forward_demodulation,[],[f19,f284]) ).
fof(f3535,plain,
( multiply(b1,inverse(b1)) != multiply(a1,inverse(a1))
| spl0_4 ),
inference(forward_demodulation,[],[f3533,f284]) ).
fof(f3536,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f3535,f195]) ).
fof(f3537,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f3536]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f20]) ).
cnf(s184,plain,
spl0_1,
inference(sat_conversion,[],[f378]) ).
cnf(s1068,plain,
spl0_2,
inference(sat_conversion,[],[f3332]) ).
cnf(s1202,plain,
spl0_3,
inference(sat_conversion,[],[f3531]) ).
cnf(s1203,plain,
spl0_4,
inference(sat_conversion,[],[f3537]) ).
cnf(s1204,plain,
$false,
inference(rat,[],[s4,s1203,s1202,s1068,s184]) ).
fof(f3538,plain,
$false,
inference(avatar_sat_refutation,[],[s1204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 27 09:16:40 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.48 Running first-order model finding
% 0.22/0.48 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
% 1.29/0.64 % (1148824)Will run a generic schedule for satisfiability detection.
% 1.29/0.64 % (1148830)% WARNING: option uhcvi not known.
% 1.29/0.64 % (1148830)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=244395671:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.29/0.64 % (1148831)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1063289550:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.29/0.64 % (1148832)dis+10_1_sil=32000:sp=arity:random_seed=1789873297:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.29/0.64 % (1148829)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3818693988_3000 on theBenchmark for (3000ds/0Mi)
% 1.29/0.64 % (1148834)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1143150638:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.29/0.64 % (1148833)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1835629504:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.29/0.64 % (1148835)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3237385577:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.29/0.64 % TRYING [1]
% 1.29/0.64 % TRYING [2]
% 1.29/0.64 % TRYING [3]
% 1.29/0.64 % TRYING [4]
% 1.29/0.64 % (1148832)Instruction limit reached!
% 1.29/0.64 % (1148832)------------------------------
% 1.29/0.64 % (1148832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.64 % (1148832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.64 % (1148832)CaDiCaL version: 2.1.3
% 1.29/0.64 % (1148832)Termination reason: Instruction limit
% 1.29/0.64 % (1148832)Termination phase: Saturation
% 1.29/0.64 % (1148832)Time elapsed: 0.093 s
% 1.29/0.64 % (1148832)Peak memory usage: 12 MB
% 1.29/0.64 % (1148832)Instructions burned: 104 (million)
% 1.29/0.64 % (1148833)Instruction limit reached!
% 1.29/0.64 % (1148833)------------------------------
% 1.29/0.64 % (1148833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.64 % (1148833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.64 % (1148833)CaDiCaL version: 2.1.3
% 1.29/0.64 % (1148833)Termination reason: Instruction limit
% 1.29/0.64 % (1148833)Termination phase: Saturation
% 1.29/0.64 % (1148833)Time elapsed: 0.104 s
% 1.29/0.64 % (1148833)Peak memory usage: 13 MB
% 1.29/0.64 % (1148833)Instructions burned: 116 (million)
% 1.29/0.64 % (1148831) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1148824-1148831"...
% 1.29/0.64 % (1148831)...printing done.
% 1.29/0.64 % (1148831)Refutation found. Thanks to Tanya!
% 1.29/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.29/0.64 % SZS output start Proof for theBenchmark
% See solution above
% 1.29/0.64 % (1148831)------------------------------
% 1.29/0.64 % (1148831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.64 % (1148831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.64 % (1148831)CaDiCaL version: 2.1.3
% 1.29/0.64 % (1148831)Termination reason: Refutation
% 1.29/0.64 % (1148831)Time elapsed: 0.122 s
% 1.29/0.64 % (1148831)Peak memory usage: 13 MB
% 1.29/0.64 % (1148831)Instructions burned: 133 (million)
% 1.29/0.64 % (1148824)Success in time 0.151 s
% 1.29/0.64 % Vampire exiting
%------------------------------------------------------------------------------