%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 10:12:05 AM UTC 2026
% Result : Unsatisfiable 3.60s 1.47s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 5 unt; 0 def)
% Number of atoms : 14 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : product(X0,inverse(X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f5,axiom,
an_element(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_of_set) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ product(X0,inverse(X1),X2)
| ~ an_element(X1)
| ~ an_element(X0)
| an_element(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
fof(f9,negated_conjecture,
~ an_element(identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_identity_is_an_element) ).
fof(f11,plain,
! [X0] :
( ~ an_element(X0)
| ~ an_element(X0)
| an_element(identity) ),
inference(resolution,[],[f6,f3]) ).
fof(f13,plain,
! [X0] :
( ~ an_element(X0)
| an_element(identity) ),
inference(duplicate_literal_removal,[],[f11]) ).
fof(f15,plain,
! [X0] : ~ an_element(X0),
inference(forward_subsumption_resolution,[],[f13,f9]) ).
fof(f20,plain,
$false,
inference(resolution,[],[f15,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 09:12:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.60/1.47 % (4144818)Input is clausal, will run a generic CNF schedule.
% 3.60/1.47 % (4144827)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=267946905:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.60/1.47 % (4144827)Refutation not found, incomplete strategy
% 3.60/1.47 % (4144827)------------------------------
% 3.60/1.47 % (4144827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.47 % (4144827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.47 % (4144827)CaDiCaL version: 2.1.3
% 3.60/1.47 % (4144827)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.47 % (4144827)Time elapsed: 0.001 s
% 3.60/1.47 % (4144827)Peak memory usage: 87 MB
% 3.60/1.47 % (4144829)dis-21_1_sil=8000:lcm=predicate:random_seed=1905210048:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.60/1.47 % (4144823)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3290798617:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.60/1.47 % (4144826)lrs+10_1_sil=8000:sp=occurrence:random_seed=584422674:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.60/1.47 % (4144824)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1838662050:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.60/1.47 % (4144825)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3968129086:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.60/1.47 % (4144826)First to succeed.
% 3.60/1.47 % (4144829)Also succeeded, but the first one will report.
% 3.60/1.47 % (4144826)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4144818"
% 3.60/1.47 % (4144828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3120993709:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.60/1.47 % (4144828)Also succeeded, but the first one will report.
% 3.60/1.47 % (4144827)------------------------------
% 3.60/1.47 % (4144827)------------------------------
% 3.60/1.47 % (4144837)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=457509477:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.60/1.47 % (4144837)Refutation not found, incomplete strategy
% 3.60/1.47 % (4144837)------------------------------
% 3.60/1.47 % (4144837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.47 % (4144837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.47 % (4144837)CaDiCaL version: 2.1.3
% 3.60/1.47 % (4144837)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.47 % (4144837)Time elapsed: 0.0000 s
% 3.60/1.47 % (4144837)Peak memory usage: 87 MB
% 3.60/1.47 % (4144826)Refutation found. Thanks to Tanya!
% 3.60/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.60/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.47 % (4144826)------------------------------
% 3.60/1.47 % (4144826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.47 % (4144826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.47 % (4144826)CaDiCaL version: 2.1.3
% 3.60/1.47 % (4144826)Termination reason: Refutation
% 3.60/1.47 % (4144826)Time elapsed: 0.001 s
% 3.60/1.47 % (4144826)Peak memory usage: 88 MB
% 3.60/1.47 % (4144826)------------------------------
% 3.60/1.47 % (4144826)------------------------------
% 3.60/1.47 % (4144818)Success in time 0.429 s
% 3.60/1.47 % Vampire exiting
%------------------------------------------------------------------------------