%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP588-1 : 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 : n001.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 10:14:55 AM UTC 2026
% Result : Unsatisfiable 3.79s 1.52s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 29 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),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(f4,plain,
! [X2,X0,X1] : double_divide(X0,multiply(X1,inverse(double_divide(double_divide(X0,X1),inverse(X2))))) = X2,
inference(forward_demodulation,[],[f1,f2]) ).
fof(f5,plain,
! [X2,X0,X1] : double_divide(X0,multiply(X1,multiply(inverse(X2),double_divide(X0,X1)))) = X2,
inference(forward_demodulation,[],[f4,f2]) ).
fof(f7,plain,
! [X2,X3,X0,X1] : double_divide(X1,multiply(multiply(X2,multiply(inverse(X0),double_divide(X1,X2))),multiply(inverse(X3),X0))) = X3,
inference(superposition,[],[f5,f5]) ).
fof(f8,plain,
! [X2,X0,X1] : inverse(X0) = multiply(multiply(X1,multiply(inverse(X0),double_divide(X2,X1))),X2),
inference(superposition,[],[f2,f5]) ).
fof(f34,plain,
! [X0,X1] : double_divide(multiply(inverse(X1),X0),inverse(X0)) = X1,
inference(superposition,[],[f7,f8]) ).
fof(f41,plain,
! [X2,X0,X1] : double_divide(multiply(inverse(X2),double_divide(X1,X0)),multiply(X0,X1)) = X2,
inference(superposition,[],[f34,f2]) ).
fof(f47,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X1),multiply(inverse(X0),X1)),
inference(superposition,[],[f2,f34]) ).
fof(f49,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(inverse(X2),multiply(multiply(X0,X1),X2)),
inference(superposition,[],[f47,f2]) ).
fof(f51,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X0),X1))) = X1,
inference(superposition,[],[f34,f47]) ).
fof(f57,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),inverse(inverse(X0))),
inference(superposition,[],[f51,f47]) ).
fof(f160,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = double_divide(inverse(X2),inverse(multiply(X0,X1))),
inference(superposition,[],[f51,f49]) ).
fof(f329,plain,
! [X0,X1] : multiply(multiply(inverse(X1),X0),X1) = X0,
inference(superposition,[],[f160,f51]) ).
fof(f345,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),double_divide(X1,inverse(X1))),
inference(superposition,[],[f329,f8]) ).
fof(f360,plain,
! [X2,X0] : multiply(inverse(X2),multiply(X0,X2)) = X0,
inference(superposition,[],[f49,f329]) ).
fof(f363,plain,
! [X2,X0] : multiply(X0,X2) = double_divide(inverse(X2),inverse(X0)),
inference(superposition,[],[f160,f329]) ).
fof(f638,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(inverse(X1),X1)) = X0,
inference(superposition,[],[f41,f345]) ).
fof(f643,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[],[f34,f345]) ).
fof(f673,plain,
! [X0,X1] : multiply(double_divide(X1,inverse(X1)),X0) = X0,
inference(forward_demodulation,[],[f643,f363]) ).
fof(f680,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f673,f57]) ).
fof(f769,plain,
! [X2,X0,X1] : double_divide(inverse(X0),multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X0))) = X2,
inference(superposition,[],[f5,f638]) ).
fof(f792,plain,
! [X2,X0] : double_divide(inverse(X0),multiply(inverse(X2),X0)) = X2,
inference(forward_demodulation,[],[f769,f680]) ).
fof(f929,plain,
! [X0,X1] : double_divide(inverse(multiply(inverse(X0),X1)),inverse(X0)) = X1,
inference(superposition,[],[f792,f47]) ).
fof(f949,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f929,f363]) ).
fof(f1206,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f949,f360]) ).
fof(f1424,plain,
multiply(a,b) != multiply(a,b),
inference(superposition,[],[f3,f1206]) ).
fof(f1425,plain,
$false,
inference(trivial_inequality_removal,[],[f1424]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP588-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 10:13:30 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 3.79/1.52 % (3333377)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.79/1.52 % (3333448)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=2424735737:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.79/1.52 % (3333450)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1432570384:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.79/1.52 % (3333451)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3977800262:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.79/1.52 % (3333449)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2344290361:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.79/1.52 % (3333447)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=2522635350:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.79/1.52 % (3333453)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3259476488:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.79/1.52 % (3333452)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2561433011:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.79/1.52 % (3333453)First to succeed.
% 3.79/1.52 % (3333453)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3333377"
% 3.79/1.52 % (3333450)Instruction limit reached!
% 3.79/1.52 % (3333450)------------------------------
% 3.79/1.52 % (3333450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.52 % (3333450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.52 % (3333450)CaDiCaL version: 2.1.3
% 3.79/1.52 % (3333450)Termination reason: Instruction limit
% 3.79/1.52 % (3333450)Termination phase: Saturation
% 3.79/1.52 % (3333450)Time elapsed: 0.082 s
% 3.79/1.52 % (3333450)Peak memory usage: 89 MB
% 3.79/1.52 % (3333450)Instructions burned: 136 (million)
% 3.79/1.52 % (3333452)Also succeeded, but the first one will report.
% 3.79/1.52 % (3333451)Instruction limit reached!
% 3.79/1.52 % (3333451)------------------------------
% 3.79/1.52 % (3333451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.52 % (3333451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.52 % (3333451)CaDiCaL version: 2.1.3
% 3.79/1.52 % (3333451)Termination reason: Instruction limit
% 3.79/1.52 % (3333451)Termination phase: Saturation
% 3.79/1.52 % (3333451)Time elapsed: 0.102 s
% 3.79/1.52 % (3333451)Peak memory usage: 90 MB
% 3.79/1.52 % (3333451)Instructions burned: 182 (million)
% 3.79/1.52 % (3333461)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4056415418:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.79/1.52 % (3333462)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1423440222:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.79/1.52 % (3333453)Refutation found. Thanks to Tanya!
% 3.79/1.52 % SZS status Unsatisfiable for theBenchmark
% 3.79/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.52 % (3333453)------------------------------
% 3.79/1.52 % (3333453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.52 % (3333453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.52 % (3333453)CaDiCaL version: 2.1.3
% 3.79/1.52 % (3333453)Termination reason: Refutation
% 3.79/1.52 % (3333453)Time elapsed: 0.037 s
% 3.79/1.52 % (3333453)Peak memory usage: 88 MB
% 3.79/1.52 % (3333453)Instructions burned: 61 (million)
% 3.79/1.52 % (3333453)------------------------------
% 3.79/1.52 % (3333453)------------------------------
% 3.79/1.52 % (3333377)Success in time 0.435 s
% 3.79/1.52 % Vampire exiting
%------------------------------------------------------------------------------