%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 10:14:45 AM UTC 2026
% Result : Unsatisfiable 0.16s 1.71s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 28 unt; 1 def)
% Number of atoms : 48 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 9 |; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f3,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f2]) ).
fof(f5,definition,
( spl0_1
<=> a2 = multiply(multiply(inverse(b2),b2),a2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( a2 != multiply(multiply(inverse(b2),b2),a2)
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f9,plain,
! [X2,X3,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(X0,X3),inverse(multiply(multiply(multiply(X1,X0),X2),X3))),
inference(superposition,[],[f1,f1]) ).
fof(f10,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f11,plain,
! [X2,X3,X0,X1] : multiply(multiply(multiply(multiply(multiply(X1,X0),X2),X3),inverse(multiply(X1,X2))),inverse(X0)) = X3,
inference(superposition,[],[f1,f1]) ).
fof(f15,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X0)))) = multiply(X1,inverse(multiply(multiply(X2,X1),inverse(X0)))),
inference(superposition,[],[f10,f10]) ).
fof(f33,plain,
! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,inverse(multiply(multiply(X0,X1),X2))))) = X2,
inference(superposition,[],[f10,f9]) ).
fof(f43,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(X3,multiply(X1,X2)),inverse(multiply(X3,X0)))) = inverse(multiply(X1,multiply(X2,inverse(X0)))),
inference(superposition,[],[f33,f10]) ).
fof(f45,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,multiply(X1,X2))))) = X2,
inference(superposition,[],[f33,f9]) ).
fof(f89,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(X1,X2),X3),inverse(multiply(X1,X3)))) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(superposition,[],[f9,f11]) ).
fof(f102,plain,
! [X2,X0] : inverse(X2) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(forward_demodulation,[],[f89,f1]) ).
fof(f111,plain,
! [X3,X0] : multiply(multiply(X3,X0),inverse(X3)) = X0,
inference(superposition,[],[f102,f45]) ).
fof(f112,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X0),X2))),
inference(superposition,[],[f102,f1]) ).
fof(f177,plain,
! [X2,X1] : inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(backward_demodulation,[],[f10,f112]) ).
fof(f178,plain,
! [X2,X3,X0] : inverse(multiply(multiply(X3,X2),inverse(multiply(X3,X0)))) = inverse(multiply(X2,inverse(X0))),
inference(backward_demodulation,[],[f15,f112]) ).
fof(f228,plain,
! [X2,X0,X1] : inverse(multiply(X1,multiply(X2,inverse(X0)))) = inverse(multiply(multiply(X1,X2),inverse(X0))),
inference(backward_demodulation,[],[f43,f178]) ).
fof(f322,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f111,f111]) ).
fof(f335,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f177,f322]) ).
fof(f353,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X1,X0))),
inference(superposition,[],[f335,f177]) ).
fof(f354,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[],[f111,f335]) ).
fof(f444,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(X0,inverse(X1))),
inference(superposition,[],[f354,f322]) ).
fof(f482,plain,
( a2 != multiply(inverse(multiply(b2,inverse(b2))),a2)
| spl0_1 ),
inference(backward_demodulation,[],[f7,f444]) ).
fof(f484,plain,
( a2 != inverse(multiply(multiply(b2,inverse(b2)),inverse(a2)))
| spl0_1 ),
inference(forward_demodulation,[],[f482,f444]) ).
fof(f509,plain,
( a2 != inverse(multiply(b2,multiply(inverse(b2),inverse(a2))))
| spl0_1 ),
inference(forward_demodulation,[],[f484,f228]) ).
fof(f524,plain,
( a2 != inverse(multiply(b2,inverse(multiply(b2,inverse(inverse(a2))))))
| spl0_1 ),
inference(forward_demodulation,[],[f509,f444]) ).
fof(f537,plain,
( a2 != inverse(inverse(inverse(inverse(a2))))
| spl0_1 ),
inference(forward_demodulation,[],[f524,f353]) ).
fof(f546,plain,
( a2 != inverse(inverse(a2))
| spl0_1 ),
inference(forward_demodulation,[],[f537,f335]) ).
fof(f555,plain,
( a2 != a2
| spl0_1 ),
inference(forward_demodulation,[],[f546,f335]) ).
fof(f556,plain,
( $false
| spl0_1 ),
inference(trivial_inequality_removal,[],[f555]) ).
fof(f557,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f556]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s7,plain,
spl0_1,
inference(sat_conversion,[],[f557]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s7]) ).
fof(f616,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP510-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 10:09:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/1.71 % (3310654)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.16/1.71 % (3310684)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2965696485:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 0.16/1.71 % (3310684)First to succeed.
% 0.16/1.71 % (3310684)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3310654"
% 0.16/1.71 % (3310679)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=1993309510:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 0.16/1.71 % (3310680)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=3839421347:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 0.16/1.71 % (3310681)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4175703220:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 0.16/1.71 % (3310683)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3355708611:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 0.16/1.71 % (3310682)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3388358185:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 0.16/1.71 % (3310685)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3416512524:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 0.16/1.71 % (3310685)Also succeeded, but the first one will report.
% 0.16/1.71 % (3310682)Also succeeded, but the first one will report.
% 0.16/1.71 % (3310683)Also succeeded, but the first one will report.
% 0.16/1.71 % (3310684)Refutation found. Thanks to Tanya!
% 0.16/1.71 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.71 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.71 % (3310684)------------------------------
% 0.16/1.71 % (3310684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.71 % (3310684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.71 % (3310684)CaDiCaL version: 2.1.3
% 0.16/1.71 % (3310684)Termination reason: Refutation
% 0.16/1.71 % (3310684)Time elapsed: 0.032 s
% 0.16/1.71 % (3310684)Peak memory usage: 89 MB
% 0.16/1.71 % (3310684)Instructions burned: 55 (million)
% 0.16/1.71 % (3310684)------------------------------
% 0.16/1.71 % (3310684)------------------------------
% 0.16/1.71 % (3310654)Success in time 0.396 s
% 0.16/1.71 % Vampire exiting
%------------------------------------------------------------------------------