%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP606-1 : 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 : n026.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 10:14:58 AM UTC 2026
% Result : Unsatisfiable 3.74s 1.52s
% Output : Refutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(inverse(double_divide(X0,inverse(double_divide(inverse(X1),double_divide(X0,X2))))),X2) = X1,
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(f5,plain,
! [X2,X0,X1] : double_divide(multiply(inverse(double_divide(inverse(X1),double_divide(X0,X2))),X0),X2) = X1,
inference(forward_demodulation,[],[f1,f2]) ).
fof(f6,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(double_divide(X0,X2),inverse(X1)),X0),X2) = X1,
inference(forward_demodulation,[],[f5,f2]) ).
fof(f7,plain,
! [X2,X3,X0,X1] : double_divide(multiply(multiply(X0,inverse(X3)),multiply(multiply(double_divide(X1,X2),inverse(X0)),X1)),X2) = X3,
inference(superposition,[],[f6,f6]) ).
fof(f9,plain,
! [X2,X0,X1] : inverse(X0) = multiply(X1,multiply(multiply(double_divide(X2,X1),inverse(X0)),X2)),
inference(superposition,[],[f2,f6]) ).
fof(f35,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X0,inverse(X1))) = X1,
inference(superposition,[],[f7,f9]) ).
fof(f41,plain,
! [X2,X0,X1] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),inverse(X2))) = X2,
inference(superposition,[],[f35,f2]) ).
fof(f48,plain,
! [X0,X1] : inverse(X0) = multiply(multiply(X1,inverse(X0)),inverse(X1)),
inference(superposition,[],[f2,f35]) ).
fof(f49,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(X2,multiply(X0,X1)),inverse(X2)),
inference(superposition,[],[f48,f2]) ).
fof(f52,plain,
! [X0,X1] : double_divide(inverse(multiply(X1,inverse(X0))),inverse(X0)) = X1,
inference(superposition,[],[f35,f48]) ).
fof(f57,plain,
! [X0,X1] : multiply(X1,inverse(X0)) = double_divide(inverse(inverse(X0)),inverse(X1)),
inference(superposition,[],[f52,f48]) ).
fof(f161,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = double_divide(inverse(multiply(X0,X1)),inverse(X2)),
inference(superposition,[],[f52,f49]) ).
fof(f330,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X1))) = X0,
inference(superposition,[],[f161,f52]) ).
fof(f346,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(inverse(X1),X1),inverse(X0)),
inference(superposition,[],[f330,f9]) ).
fof(f356,plain,
! [X2,X0] : multiply(multiply(X2,X0),inverse(X2)) = X0,
inference(superposition,[],[f49,f330]) ).
fof(f360,plain,
! [X0,X1] : multiply(X1,X0) = double_divide(inverse(X0),inverse(X1)),
inference(superposition,[],[f161,f330]) ).
fof(f640,plain,
! [X0,X1] : double_divide(multiply(X1,inverse(X1)),inverse(X0)) = X0,
inference(superposition,[],[f41,f346]) ).
fof(f645,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X1),X1)),inverse(X0)) = X0,
inference(superposition,[],[f35,f346]) ).
fof(f675,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X1)) = X0,
inference(forward_demodulation,[],[f645,f360]) ).
fof(f682,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(superposition,[],[f675,f57]) ).
fof(f771,plain,
! [X2,X0,X1] : double_divide(multiply(multiply(X0,inverse(X2)),multiply(X1,inverse(X1))),inverse(X0)) = X2,
inference(superposition,[],[f6,f640]) ).
fof(f794,plain,
! [X2,X0] : double_divide(multiply(X0,inverse(X2)),inverse(X0)) = X2,
inference(forward_demodulation,[],[f771,f682]) ).
fof(f930,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(X1,inverse(X0)))) = X1,
inference(superposition,[],[f794,f48]) ).
fof(f951,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(forward_demodulation,[],[f930,f360]) ).
fof(f1209,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f951,f356]) ).
fof(f1427,plain,
a2 != multiply(a2,multiply(inverse(b2),b2)),
inference(superposition,[],[f4,f1209]) ).
fof(f1428,plain,
a2 != multiply(a2,multiply(b2,inverse(b2))),
inference(forward_demodulation,[],[f1427,f1209]) ).
fof(f1496,plain,
$false,
inference(forward_subsumption_resolution,[],[f1428,f682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP606-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 10:12:42 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 3.74/1.52 % (2607424)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.74/1.52 % (2607527)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3672346400:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.74/1.52 % (2607530)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1138388056:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.74/1.52 % (2607528)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1742751907:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.74/1.52 % (2607531)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3637962450:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.74/1.52 % (2607525)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2525657493:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.74/1.52 % (2607524)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=3243054582:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.74/1.52 % (2607523)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=2873042113:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.74/1.52 % (2607527)Instruction limit reached!
% 3.74/1.52 % (2607527)------------------------------
% 3.74/1.52 % (2607527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.52 % (2607527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.52 % (2607527)CaDiCaL version: 2.1.3
% 3.74/1.52 % (2607527)Termination reason: Instruction limit
% 3.74/1.52 % (2607527)Termination phase: Saturation
% 3.74/1.52 % (2607527)Time elapsed: 0.045 s
% 3.74/1.52 % (2607527)Peak memory usage: 88 MB
% 3.74/1.52 % (2607531)First to succeed.
% 3.74/1.52 % (2607527)Instructions burned: 138 (million)
% 3.74/1.52 % (2607531)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2607424"
% 3.74/1.52 % (2607530)Also succeeded, but the first one will report.
% 3.74/1.52 % (2607528)Instruction limit reached!
% 3.74/1.52 % (2607528)------------------------------
% 3.74/1.52 % (2607528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.52 % (2607528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.52 % (2607528)CaDiCaL version: 2.1.3
% 3.74/1.52 % (2607528)Termination reason: Instruction limit
% 3.74/1.52 % (2607528)Termination phase: Saturation
% 3.74/1.52 % (2607528)Time elapsed: 0.100 s
% 3.74/1.52 % (2607528)Peak memory usage: 90 MB
% 3.74/1.52 % (2607528)Instructions burned: 181 (million)
% 3.74/1.52 % (2607551)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2100109720:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.74/1.52 % (2607572)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=189126989:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.74/1.52 % (2607531)Refutation found. Thanks to Tanya!
% 3.74/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.74/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.74/1.52 % (2607531)------------------------------
% 3.74/1.52 % (2607531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.74/1.52 % (2607531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.74/1.52 % (2607531)CaDiCaL version: 2.1.3
% 3.74/1.52 % (2607531)Termination reason: Refutation
% 3.74/1.52 % (2607531)Time elapsed: 0.039 s
% 3.74/1.52 % (2607531)Peak memory usage: 88 MB
% 3.74/1.52 % (2607531)Instructions burned: 64 (million)
% 3.74/1.52 % (2607531)------------------------------
% 3.74/1.52 % (2607531)------------------------------
% 3.74/1.52 % (2607424)Success in time 0.434 s
% 3.74/1.52 % Vampire exiting
%------------------------------------------------------------------------------