%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 10:12:39 AM UTC 2026
% Result : Unsatisfiable 2.01s 0.89s
% Output : Refutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 21 unt; 6 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 122 ( 60 ~; 56 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(e_1,X0,X1)
| product(e_2,X0,X1)
| product(e_3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f7,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f8,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f16,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f17,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(X2,X3,e_2)
| ~ product(X2,X0,e_3)
| ~ product(e_2,X3,X1) ),
inference(resolution,[],[f9,f17]) ).
fof(f48,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f13,f16]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f14,f16]) ).
fof(f55,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,e_1,X0)
| product(e_2,e_1,X0)
| product(e_3,e_1,X0) ),
inference(resolution,[],[f1,f3]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(e_2,X1,e_3)
| ~ product(X0,e_3,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[],[f36,f16]) ).
fof(f112,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(resolution,[],[f55,f4]) ).
fof(f113,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_3,e_1,e_3) ),
inference(resolution,[],[f55,f5]) ).
fof(f115,definition,
( spl0_6
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f117,plain,
( product(e_3,e_1,e_3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f119,definition,
( spl0_7
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f121,plain,
( product(e_2,e_1,e_3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f123,definition,
( spl0_8
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f125,plain,
( product(e_1,e_1,e_3)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f126,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f113,f123,f119,f115]) ).
fof(f128,definition,
( spl0_9
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f130,plain,
( product(e_3,e_1,e_2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl0_10
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f134,plain,
( product(e_2,e_1,e_2)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f136,definition,
( spl0_11
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f138,plain,
( product(e_1,e_1,e_2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(avatar_split_clause,[],[f112,f136,f132,f128]) ).
fof(f140,plain,
( ! [X0] :
( ~ product(X0,e_1,e_2)
| ~ product(X0,e_3,e_3) )
| ~ spl0_7 ),
inference(resolution,[],[f121,f78]) ).
fof(f284,plain,
( equalish(e_1,e_3)
| ~ spl0_8 ),
inference(resolution,[],[f125,f48]) ).
fof(f288,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f284,f7]) ).
fof(f289,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f288]) ).
fof(f296,plain,
( ~ product(e_3,e_3,e_3)
| ~ spl0_7
| ~ spl0_9 ),
inference(resolution,[],[f130,f140]) ).
fof(f302,plain,
( $false
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f296,f16]) ).
fof(f303,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f302]) ).
fof(f313,plain,
( equalish(e_1,e_2)
| ~ spl0_11 ),
inference(resolution,[],[f138,f48]) ).
fof(f317,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f313,f6]) ).
fof(f318,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f333,plain,
( equalish(e_3,e_1)
| ~ spl0_6 ),
inference(resolution,[],[f117,f51]) ).
fof(f334,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f333,f10]) ).
fof(f335,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f352,plain,
( equalish(e_2,e_1)
| ~ spl0_10 ),
inference(resolution,[],[f134,f51]) ).
fof(f353,plain,
( $false
| ~ spl0_10 ),
inference(forward_subsumption_resolution,[],[f352,f8]) ).
fof(f354,plain,
~ spl0_10,
inference(avatar_contradiction_clause,[],[f353]) ).
cnf(s6,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f126]) ).
cnf(s7,plain,
( spl0_9
| spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f139]) ).
cnf(s25,plain,
~ spl0_8,
inference(sat_conversion,[],[f289]) ).
cnf(s26,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f303]) ).
cnf(s29,plain,
~ spl0_11,
inference(sat_conversion,[],[f318]) ).
cnf(s34,plain,
~ spl0_6,
inference(sat_conversion,[],[f335]) ).
cnf(s35,plain,
~ spl0_10,
inference(sat_conversion,[],[f354]) ).
cnf(s43,plain,
spl0_9,
inference(rat,[],[s7,s29,s35]) ).
cnf(s44,plain,
~ spl0_7,
inference(rat,[],[s26,s43]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s6,s25,s44,s34]) ).
fof(f355,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP123-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 09:19:36 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.33 Running first-order theorem proving
% 0.06/0.33 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
% 2.01/0.89 % (2110512)Input is clausal, will run a generic CNF schedule.
% 2.01/0.89 % (2110522)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2644377291:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.01/0.89 % (2110523)dis-21_1_sil=8000:lcm=predicate:random_seed=632211921: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)
% 2.01/0.89 % (2110517)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=330524473:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.01/0.89 % (2110519)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4101779635:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.01/0.89 % (2110521)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4197135988:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.01/0.89 % (2110520)lrs+10_1_sil=8000:sp=occurrence:random_seed=3545777294:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.01/0.89 % (2110518)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3954041282:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.01/0.89 % (2110520)Refutation not found, incomplete strategy
% 2.01/0.89 % (2110520)------------------------------
% 2.01/0.89 % (2110520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/0.89 % (2110520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.89 % (2110520)CaDiCaL version: 2.1.3
% 2.01/0.89 % (2110520)Termination reason: Refutation not found, incomplete strategy
% 2.01/0.89 % (2110520)Time elapsed: 0.0000 s
% 2.01/0.89 % (2110520)Peak memory usage: 86 MB
% 2.01/0.89 % (2110522)First to succeed.
% 2.01/0.89 % (2110522)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2110512"
% 2.01/0.89 % (2110521)Also succeeded, but the first one will report.
% 2.01/0.89 % (2110523)Also succeeded, but the first one will report.
% 2.01/0.89 % (2110520)------------------------------
% 2.01/0.89 % (2110520)------------------------------
% 2.01/0.89 % (2110522)Refutation found. Thanks to Tanya!
% 2.01/0.89 % SZS status Unsatisfiable for theBenchmark
% 2.01/0.89 % SZS output start Proof for theBenchmark
% See solution above
% 2.01/0.89 % (2110522)------------------------------
% 2.01/0.89 % (2110522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/0.89 % (2110522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.89 % (2110522)CaDiCaL version: 2.1.3
% 2.01/0.89 % (2110522)Termination reason: Refutation
% 2.01/0.89 % (2110522)Time elapsed: 0.004 s
% 2.01/0.89 % (2110522)Peak memory usage: 89 MB
% 2.01/0.89 % (2110522)Instructions burned: 10 (million)
% 2.01/0.89 % (2110522)------------------------------
% 2.01/0.89 % (2110522)------------------------------
% 2.01/0.89 % (2110512)Success in time 0.265 s
% 2.01/0.89 % Vampire exiting
%------------------------------------------------------------------------------