%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP592-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 0.16s 1.60s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 38 unt; 1 def)
% Number of atoms : 44 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 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 : 73 ( 0 sgn 73 !; 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/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f5,definition,
( spl0_1
<=> multiply(a,b) = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f7,plain,
( multiply(a,b) != multiply(b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f5]) ).
fof(f8,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f5]) ).
fof(f9,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(f10,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X2),X0),double_divide(X0,X1)),X1) = X2,
inference(forward_demodulation,[],[f9,f2]) ).
fof(f12,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,[],[f10,f10]) ).
fof(f13,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X1,multiply(multiply(inverse(X0),X2),double_divide(X2,X1))),
inference(superposition,[],[f2,f10]) ).
fof(f45,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X0),inverse(X1)) = X1,
inference(superposition,[],[f12,f13]) ).
fof(f56,plain,
! [X2,X0,X1] : inverse(X1) = multiply(inverse(X0),multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),X0)),
inference(superposition,[],[f13,f45]) ).
fof(f57,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),X0),inverse(X0)) = X1,
inference(superposition,[],[f10,f45]) ).
fof(f58,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),multiply(inverse(X1),X1)),
inference(superposition,[],[f2,f45]) ).
fof(f59,plain,
! [X0,X1] : double_divide(multiply(inverse(X1),X0),inverse(X0)) = X1,
inference(forward_demodulation,[],[f57,f58]) ).
fof(f60,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(X0),multiply(inverse(X1),X0)),
inference(forward_demodulation,[],[f56,f58]) ).
fof(f76,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X1),X1))) = X0,
inference(superposition,[],[f59,f58]) ).
fof(f80,plain,
! [X0,X1] : double_divide(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(superposition,[],[f45,f58]) ).
fof(f122,plain,
! [X2,X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),inverse(multiply(inverse(X2),X2))),
inference(superposition,[],[f76,f2]) ).
fof(f126,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(inverse(X1),inverse(X0)),X0),inverse(multiply(inverse(X2),X2))) = X1,
inference(superposition,[],[f10,f76]) ).
fof(f133,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(backward_demodulation,[],[f126,f122]) ).
fof(f178,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f76,f80]) ).
fof(f225,plain,
! [X2,X0,X1] : inverse(X1) = multiply(X2,multiply(multiply(inverse(X0),X0),double_divide(X1,X2))),
inference(superposition,[],[f13,f178]) ).
fof(f230,plain,
! [X0,X1] : inverse(X1) = double_divide(X1,multiply(inverse(X0),X0)),
inference(superposition,[],[f133,f178]) ).
fof(f239,plain,
! [X0,X1] : inverse(X1) = double_divide(X1,inverse(multiply(inverse(X0),X0))),
inference(superposition,[],[f230,f58]) ).
fof(f246,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(inverse(X1),X1),X0),
inference(superposition,[],[f2,f230]) ).
fof(f270,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[],[f76,f239]) ).
fof(f271,plain,
! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1)),
inference(backward_demodulation,[],[f122,f239]) ).
fof(f314,plain,
! [X2,X0,X1] : inverse(X1) = multiply(X2,multiply(multiply(inverse(X0),X0),inverse(multiply(X2,X1)))),
inference(backward_demodulation,[],[f225,f271]) ).
fof(f377,plain,
! [X0,X1] : multiply(multiply(inverse(X1),X1),X0) = X0,
inference(backward_demodulation,[],[f246,f270]) ).
fof(f459,plain,
! [X2,X1] : inverse(X1) = multiply(X2,inverse(multiply(X2,X1))),
inference(backward_demodulation,[],[f314,f377]) ).
fof(f559,plain,
! [X0,X1] : multiply(inverse(X1),multiply(X0,X1)) = X0,
inference(superposition,[],[f60,f270]) ).
fof(f596,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[],[f559,f270]) ).
fof(f707,plain,
! [X0,X1] : multiply(multiply(X1,X0),inverse(X0)) = X1,
inference(superposition,[],[f596,f459]) ).
fof(f1111,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f596,f707]) ).
fof(f1114,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f7,f1111]) ).
fof(f1115,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1114]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f8]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1115]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f1121,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP592-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:08:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.16/1.60 % (729283)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.16/1.60 % (729308)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=778686215:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.16/1.60 % (729312)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=581582118:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.16/1.60 % (729309)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2140948953:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.16/1.60 % (729310)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=756034780:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.16/1.60 % (729307)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=4105116271:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.16/1.60 % (729313)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1358599966:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.16/1.60 % (729311)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=226392993:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.16/1.60 % (729312)First to succeed.
% 0.16/1.60 % (729312)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-729283"
% 0.16/1.60 % (729310)Instruction limit reached!
% 0.16/1.60 % (729310)------------------------------
% 0.16/1.60 % (729310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.60 % (729310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.60 % (729310)CaDiCaL version: 2.1.3
% 0.16/1.60 % (729310)Termination reason: Instruction limit
% 0.16/1.60 % (729310)Termination phase: Saturation
% 0.16/1.60 % (729310)Time elapsed: 0.077 s
% 0.16/1.60 % (729310)Peak memory usage: 88 MB
% 0.16/1.60 % (729310)Instructions burned: 137 (million)
% 0.16/1.60 % (729313)Also succeeded, but the first one will report.
% 0.16/1.60 % (729311)Instruction limit reached!
% 0.16/1.60 % (729311)------------------------------
% 0.16/1.60 % (729311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.60 % (729311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.60 % (729311)CaDiCaL version: 2.1.3
% 0.16/1.60 % (729311)Termination reason: Instruction limit
% 0.16/1.60 % (729311)Termination phase: Saturation
% 0.16/1.60 % (729311)Time elapsed: 0.115 s
% 0.16/1.60 % (729311)Peak memory usage: 90 MB
% 0.16/1.60 % (729311)Instructions burned: 181 (million)
% 0.16/1.60 % (729321)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2616192686:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 0.16/1.60 % (729312)Refutation found. Thanks to Tanya!
% 0.16/1.60 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.60 % (729312)------------------------------
% 0.16/1.60 % (729312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.60 % (729312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.60 % (729312)CaDiCaL version: 2.1.3
% 0.16/1.60 % (729312)Termination reason: Refutation
% 0.16/1.60 % (729312)Time elapsed: 0.055 s
% 0.16/1.60 % (729312)Peak memory usage: 89 MB
% 0.16/1.60 % (729312)Instructions burned: 88 (million)
% 0.16/1.60 % (729312)------------------------------
% 0.16/1.60 % (729312)------------------------------
% 0.16/1.60 % (729283)Success in time 0.475 s
% 0.16/1.60 % Vampire exiting
%------------------------------------------------------------------------------