%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP586-1 : 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 : n012.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 2.34s 0.95s
% Output : Refutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 44 ( 44 !; 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/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(X0,multiply(X1,inverse(double_divide(double_divide(X0,X1),inverse(X2))))) = X2,
inference(forward_demodulation,[],[f1,f2]) ).
fof(f6,plain,
! [X2,X0,X1] : double_divide(X0,multiply(X1,multiply(inverse(X2),double_divide(X0,X1)))) = X2,
inference(forward_demodulation,[],[f5,f2]) ).
fof(f8,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,[],[f6,f6]) ).
fof(f9,plain,
! [X2,X0,X1] : inverse(X0) = multiply(multiply(X1,multiply(inverse(X0),double_divide(X2,X1))),X2),
inference(superposition,[],[f2,f6]) ).
fof(f35,plain,
! [X0,X1] : double_divide(multiply(inverse(X1),X0),inverse(X0)) = X1,
inference(superposition,[],[f8,f9]) ).
fof(f48,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X1),multiply(inverse(X0),X1)),
inference(superposition,[],[f2,f35]) ).
fof(f50,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(inverse(X2),multiply(multiply(X0,X1),X2)),
inference(superposition,[],[f48,f2]) ).
fof(f52,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X0),X1))) = X1,
inference(superposition,[],[f35,f48]) ).
fof(f58,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),inverse(inverse(X0))),
inference(superposition,[],[f52,f48]) ).
fof(f161,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = double_divide(inverse(X2),inverse(multiply(X0,X1))),
inference(superposition,[],[f52,f50]) ).
fof(f330,plain,
! [X0,X1] : multiply(multiply(inverse(X1),X0),X1) = X0,
inference(superposition,[],[f161,f52]) ).
fof(f346,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X0),double_divide(X1,inverse(X1))),
inference(superposition,[],[f330,f9]) ).
fof(f364,plain,
! [X2,X0] : multiply(X0,X2) = double_divide(inverse(X2),inverse(X0)),
inference(superposition,[],[f161,f330]) ).
fof(f645,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[],[f35,f346]) ).
fof(f674,plain,
! [X0,X1] : multiply(double_divide(X1,inverse(X1)),X0) = X0,
inference(forward_demodulation,[],[f645,f364]) ).
fof(f681,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f674,f58]) ).
fof(f718,plain,
a2 != a2,
inference(superposition,[],[f4,f681]) ).
fof(f741,plain,
$false,
inference(trivial_inequality_removal,[],[f718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP586-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 10:07:20 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.33 Running first-order theorem proving
% 0.03/0.33 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
% 2.34/0.95 % (2146412)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.34/0.95 % (2146442)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3166217680:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.34/0.95 % (2146446)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3753738322:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.34/0.95 % (2146443)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2619498376:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.34/0.95 % (2146438)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=1398992350:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.34/0.95 % (2146440)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2173419324:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.34/0.95 % (2146439)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=1870140571:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.34/0.95 % (2146444)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2353318810:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.34/0.95 % (2146446)First to succeed.
% 2.34/0.95 % (2146446)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2146412"
% 2.34/0.95 % (2146444)Also succeeded, but the first one will report.
% 2.34/0.95 % (2146443)Also succeeded, but the first one will report.
% 2.34/0.95 % (2146442)Also succeeded, but the first one will report.
% 2.34/0.95 % (2146446)Refutation found. Thanks to Tanya!
% 2.34/0.95 % SZS status Unsatisfiable for theBenchmark
% 2.34/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.34/0.95 % (2146446)------------------------------
% 2.34/0.95 % (2146446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.34/0.95 % (2146446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.34/0.95 % (2146446)CaDiCaL version: 2.1.3
% 2.34/0.95 % (2146446)Termination reason: Refutation
% 2.34/0.95 % (2146446)Time elapsed: 0.012 s
% 2.34/0.95 % (2146446)Peak memory usage: 88 MB
% 2.34/0.95 % (2146446)Instructions burned: 35 (million)
% 2.34/0.95 % (2146446)------------------------------
% 2.34/0.95 % (2146446)------------------------------
% 2.34/0.95 % (2146412)Success in time 0.292 s
% 2.34/0.95 % Vampire exiting
%------------------------------------------------------------------------------