%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP590-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 10:14:56 AM UTC 2026
% Result : Unsatisfiable 3.32s 1.24s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 35 unt; 1 def)
% Number of atoms : 43 ( 32 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 3 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f4,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f3]) ).
fof(f6,definition,
( spl0_1
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f8,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f6]) ).
fof(f9,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f4,f6]) ).
fof(f10,plain,
! [X2,X0,X1] : double_divide(multiply(inverse(double_divide(X0,inverse(X2))),double_divide(X0,X1)),X1) = X2,
inference(backward_demodulation,[],[f1,f2]) ).
fof(f11,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X2),X0),double_divide(X0,X1)),X1) = X2,
inference(forward_demodulation,[],[f10,f2]) ).
fof(f12,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = double_divide(multiply(multiply(multiply(X0,X1),X2),double_divide(X2,X3)),X3),
inference(superposition,[],[f11,f2]) ).
fof(f13,plain,
! [X2,X3,X0,X1] : double_divide(multiply(multiply(inverse(X1),multiply(multiply(inverse(X0),X2),double_divide(X2,X3))),X0),X3) = X1,
inference(superposition,[],[f11,f11]) ).
fof(f14,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X1,multiply(multiply(inverse(X0),X2),double_divide(X2,X1))),
inference(superposition,[],[f2,f11]) ).
fof(f46,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X0),inverse(X1)) = X1,
inference(superposition,[],[f13,f14]) ).
fof(f58,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),X0),inverse(X0)) = X1,
inference(superposition,[],[f11,f46]) ).
fof(f59,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),multiply(inverse(X1),X1)),
inference(superposition,[],[f2,f46]) ).
fof(f60,plain,
! [X0,X1] : double_divide(multiply(inverse(X1),X0),inverse(X0)) = X1,
inference(forward_demodulation,[],[f58,f59]) ).
fof(f77,plain,
! [X0,X1] : double_divide(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[],[f46,f59]) ).
fof(f78,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X1),X1))) = X0,
inference(superposition,[],[f60,f59]) ).
fof(f139,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),inverse(multiply(inverse(X2),X2))),
inference(superposition,[],[f78,f2]) ).
fof(f143,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f77,f78]) ).
fof(f145,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X1),inverse(X0)),X0),inverse(multiply(inverse(X2),X2))) = X1,
inference(superposition,[],[f11,f78]) ).
fof(f152,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(backward_demodulation,[],[f145,f139]) ).
fof(f221,plain,
! [X2,X3,X0,X1] : double_divide(X1,inverse(X1)) = double_divide(multiply(multiply(multiply(inverse(X0),X0),X2),double_divide(X2,X3)),X3),
inference(superposition,[],[f12,f143]) ).
fof(f222,plain,
! [X0,X1] : double_divide(X1,inverse(X1)) = double_divide(X0,inverse(X0)),
inference(forward_demodulation,[],[f221,f12]) ).
fof(f227,plain,
! [X0,X1] : inverse(X1) = double_divide(X1,multiply(inverse(X0),X0)),
inference(superposition,[],[f152,f143]) ).
fof(f271,plain,
! [X0,X1] : multiply(inverse(X1),X1) = double_divide(X0,inverse(X0)),
inference(superposition,[],[f46,f222]) ).
fof(f384,plain,
! [X0,X1] : double_divide(inverse(X1),inverse(double_divide(X0,inverse(X0)))) = X1,
inference(superposition,[],[f78,f271]) ).
fof(f397,plain,
! [X0,X1] : inverse(X1) = double_divide(X1,double_divide(X0,inverse(X0))),
inference(superposition,[],[f152,f271]) ).
fof(f401,plain,
( ! [X0] : a2 != multiply(double_divide(X0,inverse(X0)),a2)
| spl0_1 ),
inference(superposition,[],[f8,f271]) ).
fof(f431,plain,
! [X0,X1] : double_divide(inverse(X1),multiply(inverse(X0),X0)) = X1,
inference(forward_demodulation,[],[f384,f2]) ).
fof(f588,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(double_divide(X1,inverse(X1)),X0),
inference(superposition,[],[f2,f397]) ).
fof(f611,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f227,f431]) ).
fof(f627,plain,
! [X0,X1] : multiply(double_divide(X1,inverse(X1)),X0) = X0,
inference(backward_demodulation,[],[f588,f611]) ).
fof(f660,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f401,f627]) ).
fof(f677,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f660]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f9]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f677]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f698,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP590-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 10:08:02 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.32/1.24 % (728575)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.32/1.24 % (728623)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3441729090:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.32/1.24 % (728626)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4242998186:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.32/1.24 % (728624)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2374630402:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.32/1.24 % (728620)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=578163752:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.32/1.24 % (728621)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2391108918:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.32/1.24 % (728619)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2466777497:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.32/1.24 % (728625)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2563031251:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.32/1.24 % (728625)First to succeed.
% 3.32/1.24 % (728625)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-728575"
% 3.32/1.24 % (728623)Also succeeded, but the first one will report.
% 3.32/1.24 % (728624)Also succeeded, but the first one will report.
% 3.32/1.24 % (728625)Refutation found. Thanks to Tanya!
% 3.32/1.24 % SZS status Unsatisfiable for theBenchmark
% 3.32/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.32/1.24 % (728625)------------------------------
% 3.32/1.24 % (728625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.24 % (728625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.24 % (728625)CaDiCaL version: 2.1.3
% 3.32/1.24 % (728625)Termination reason: Refutation
% 3.32/1.24 % (728625)Time elapsed: 0.045 s
% 3.32/1.24 % (728625)Peak memory usage: 90 MB
% 3.32/1.24 % (728625)Instructions burned: 68 (million)
% 3.32/1.24 % (728625)------------------------------
% 3.32/1.24 % (728625)------------------------------
% 3.32/1.24 % (728575)Success in time 0.405 s
% 3.32/1.24 % Vampire exiting
%------------------------------------------------------------------------------