%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP509-1 : 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 : n008.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 3.55s 1.47s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 40 unt; 3 def)
% Number of atoms : 66 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 12 ~; 10 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(multiply(X0,X1),X2),inverse(multiply(X0,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f4,definition,
( spl0_1
<=> multiply(inverse(a1),a1) = multiply(inverse(b1),b1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f6,plain,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| spl0_1 ),
inference(avatar_component_clause,[],[f4]) ).
fof(f7,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2,f4]) ).
fof(f8,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(f9,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(multiply(X1,X0),inverse(multiply(X1,X2))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f10,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(f17,plain,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(X1,inverse(multiply(multiply(X3,multiply(X1,X2)),inverse(multiply(X3,X0))))))) = X2,
inference(superposition,[],[f1,f9]) ).
fof(f32,plain,
! [X2,X0,X1] : inverse(multiply(X0,multiply(X1,inverse(multiply(multiply(X0,X1),X2))))) = X2,
inference(superposition,[],[f9,f8]) ).
fof(f42,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,[],[f32,f9]) ).
fof(f44,plain,
! [X2,X0,X1] : inverse(multiply(multiply(X0,X1),inverse(multiply(X0,multiply(X1,X2))))) = X2,
inference(superposition,[],[f32,f8]) ).
fof(f52,plain,
! [X2,X0,X1] : multiply(X0,inverse(multiply(X1,inverse(multiply(X1,multiply(X2,inverse(X0))))))) = X2,
inference(backward_demodulation,[],[f17,f42]) ).
fof(f88,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,[],[f8,f10]) ).
fof(f101,plain,
! [X2,X0] : inverse(X2) = multiply(multiply(X0,inverse(X2)),inverse(X0)),
inference(forward_demodulation,[],[f88,f1]) ).
fof(f110,plain,
! [X3,X0] : multiply(multiply(X3,X0),inverse(X3)) = X0,
inference(superposition,[],[f101,f44]) ).
fof(f111,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(X0,inverse(multiply(multiply(X1,X0),X2))),
inference(superposition,[],[f101,f1]) ).
fof(f115,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),
inference(superposition,[],[f101,f101]) ).
fof(f121,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),inverse(multiply(X1,inverse(X1)))),
inference(superposition,[],[f1,f101]) ).
fof(f122,plain,
! [X2,X0,X1] : inverse(multiply(X1,X2)) = multiply(multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))),inverse(X2)),
inference(superposition,[],[f10,f101]) ).
fof(f133,plain,
! [X2,X0,X1] : inverse(multiply(inverse(X0),inverse(multiply(multiply(X1,inverse(X0)),multiply(inverse(X1),X2))))) = X2,
inference(superposition,[],[f44,f101]) ).
fof(f137,plain,
! [X2,X1] : inverse(multiply(X1,X2)) = multiply(inverse(X1),inverse(X2)),
inference(backward_demodulation,[],[f122,f115]) ).
fof(f176,plain,
! [X2,X1] : inverse(multiply(X1,inverse(multiply(X1,X2)))) = X2,
inference(backward_demodulation,[],[f9,f111]) ).
fof(f178,plain,
! [X2,X1] : inverse(inverse(multiply(X1,multiply(inverse(X1),X2)))) = X2,
inference(backward_demodulation,[],[f133,f111]) ).
fof(f184,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X0,multiply(X1,inverse(X1)))),
inference(backward_demodulation,[],[f121,f137]) ).
fof(f230,plain,
! [X2,X0] : multiply(X0,multiply(X2,inverse(X0))) = X2,
inference(backward_demodulation,[],[f52,f176]) ).
fof(f321,plain,
! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
inference(superposition,[],[f110,f110]) ).
fof(f334,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f176,f321]) ).
fof(f338,plain,
! [X2,X1] : multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(backward_demodulation,[],[f178,f334]) ).
fof(f352,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X1,X0))),
inference(superposition,[],[f334,f176]) ).
fof(f353,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(superposition,[],[f110,f334]) ).
fof(f359,plain,
! [X0,X1] : multiply(X1,X0) = multiply(X0,inverse(inverse(X1))),
inference(superposition,[],[f338,f230]) ).
fof(f364,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f359,f334]) ).
fof(f404,plain,
( multiply(inverse(a1),a1) != multiply(b1,inverse(b1))
| spl0_1 ),
inference(superposition,[],[f6,f364]) ).
fof(f408,definition,
( spl0_2
<=> multiply(inverse(a1),a1) = multiply(b1,inverse(b1)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f410,plain,
( multiply(inverse(a1),a1) != multiply(b1,inverse(b1))
| spl0_2 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f411,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f404,f4,f408]) ).
fof(f436,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(X0,inverse(X1))),
inference(superposition,[],[f353,f321]) ).
fof(f473,plain,
( multiply(b1,inverse(b1)) != inverse(multiply(a1,inverse(a1)))
| spl0_2 ),
inference(backward_demodulation,[],[f410,f436]) ).
fof(f478,definition,
( spl0_3
<=> multiply(b1,inverse(b1)) = inverse(multiply(a1,inverse(a1))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f480,plain,
( multiply(b1,inverse(b1)) != inverse(multiply(a1,inverse(a1)))
| spl0_3 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f481,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f473,f408,f478]) ).
fof(f872,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X1))) = multiply(X0,inverse(X0)),
inference(superposition,[],[f352,f184]) ).
fof(f887,plain,
( $false
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f480,f872]) ).
fof(f888,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f887]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f7]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f411]) ).
cnf(s4,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f481]) ).
cnf(s6,plain,
spl0_3,
inference(sat_conversion,[],[f888]) ).
cnf(s7,plain,
spl0_2,
inference(rat,[],[s4,s6]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s2,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
fof(f914,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP509-1 : 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 : n008.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 10:07:09 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.46 Running first-order theorem proving
% 0.13/0.46 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
% 3.55/1.47 % (999621)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.55/1.47 % (999632)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=868215283:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.55/1.47 % (999632)First to succeed.
% 3.55/1.47 % (999632)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-999621"
% 3.55/1.47 % (999628)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=2292402229:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.55/1.47 % (999629)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2780873439:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.55/1.47 % (999627)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=1122907259:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.55/1.47 % (999630)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1305173318:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.55/1.47 % (999633)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=763386022:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.55/1.47 % (999631)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3424473927:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.55/1.47 % (999633)Also succeeded, but the first one will report.
% 3.55/1.47 % (999631)Also succeeded, but the first one will report.
% 3.55/1.47 % (999632)Refutation found. Thanks to Tanya!
% 3.55/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.55/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.47 % (999632)------------------------------
% 3.55/1.47 % (999632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.47 % (999632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.47 % (999632)CaDiCaL version: 2.1.3
% 3.55/1.47 % (999632)Termination reason: Refutation
% 3.55/1.47 % (999632)Time elapsed: 0.032 s
% 3.55/1.47 % (999632)Peak memory usage: 89 MB
% 3.55/1.47 % (999632)Instructions burned: 66 (million)
% 3.55/1.47 % (999632)------------------------------
% 3.55/1.47 % (999632)------------------------------
% 3.55/1.47 % (999621)Success in time 0.415 s
% 3.55/1.47 % Vampire exiting
%------------------------------------------------------------------------------