%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 2.43s 1.23s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 60 ( 19 unt; 5 def)
% Number of atoms : 148 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 77 ~; 83 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f22,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f24,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f25,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f26,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( ~ product(X3,X1,X2)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f30,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f31,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
fof(f32,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X5,X4,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X0,X1,X2)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X0)
| equalish(X3,X0) ),
inference(factoring,[],[f31]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X0)
| equalish(X2,X1) ),
inference(factoring,[],[f32]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ product(X0,X2,X0)
| ~ product(X0,X1,X0)
| equalish(X1,X2) ),
inference(factoring,[],[f37]) ).
fof(f60,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f30,f50]) ).
fof(f83,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f29,f30]) ).
fof(f106,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(e_3)
| equalish(X0,e_3) ),
inference(resolution,[],[f26,f60]) ).
fof(f116,plain,
! [X0] :
( product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3) ),
inference(forward_subsumption_resolution,[],[f106,f19]) ).
fof(f149,plain,
! [X0,X1] :
( product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| ~ product(e_2,X0,e_3)
| ~ product(e_2,X1,e_2)
| equalish(e_3,e_2) ),
inference(resolution,[],[f116,f33]) ).
fof(f159,plain,
! [X0,X1] :
( product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3)
| ~ product(e_2,X0,e_3)
| ~ product(e_2,X1,e_2) ),
inference(forward_subsumption_resolution,[],[f149,f25]) ).
fof(f163,definition,
( spl0_7
<=> ! [X1] : ~ product(e_2,X1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f164,plain,
( ! [X1] : ~ product(e_2,X1,e_2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f166,definition,
( spl0_8
<=> ! [X0] :
( product(e_3,X0,e_1)
| ~ product(e_2,X0,e_3)
| equalish(X0,e_3)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f167,plain,
( ! [X0] :
( product(e_3,X0,e_1)
| ~ product(e_2,X0,e_3)
| equalish(X0,e_3)
| ~ group_element(X0) )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f168,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f159,f166,f163]) ).
fof(f193,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f164,f30]) ).
fof(f194,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f284,definition,
( spl0_18
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f285,plain,
( ~ product(e_2,e_1,e_3)
| spl0_18 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f297,definition,
( spl0_20
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f298,plain,
( product(e_2,e_1,e_2)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f300,definition,
( spl0_21
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f301,plain,
( product(e_2,e_1,e_1)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f394,plain,
( equalish(e_3,e_1)
| ~ product(e_2,e_1,e_3)
| equalish(e_1,e_3)
| ~ group_element(e_1)
| ~ spl0_8 ),
inference(resolution,[],[f83,f167]) ).
fof(f395,plain,
( ~ product(e_2,e_1,e_3)
| equalish(e_1,e_3)
| ~ group_element(e_1)
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f394,f24]) ).
fof(f403,plain,
( ~ product(e_2,e_1,e_3)
| ~ group_element(e_1)
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f395,f21]) ).
fof(f408,plain,
( ~ product(e_2,e_1,e_3)
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f403,f17]) ).
fof(f413,plain,
( ~ spl0_18
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f408,f166,f284]) ).
fof(f442,plain,
( ~ group_element(e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_18 ),
inference(resolution,[],[f285,f26]) ).
fof(f443,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| ~ group_element(e_2)
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f442,f17]) ).
fof(f444,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f443,f18]) ).
fof(f445,plain,
( spl0_20
| spl0_21
| spl0_18 ),
inference(avatar_split_clause,[],[f444,f284,f300,f297]) ).
fof(f473,plain,
( equalish(e_1,e_2)
| ~ spl0_20 ),
inference(resolution,[],[f298,f60]) ).
fof(f478,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f473,f20]) ).
fof(f479,plain,
~ spl0_20,
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f516,plain,
( equalish(e_2,e_1)
| ~ spl0_21 ),
inference(resolution,[],[f301,f83]) ).
fof(f517,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f516,f22]) ).
fof(f518,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[],[f517]) ).
cnf(s5,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f168]) ).
cnf(s8,plain,
~ spl0_7,
inference(sat_conversion,[],[f194]) ).
cnf(s21,plain,
( ~ spl0_8
| ~ spl0_18 ),
inference(sat_conversion,[],[f413]) ).
cnf(s25,plain,
( spl0_18
| spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f445]) ).
cnf(s27,plain,
~ spl0_20,
inference(sat_conversion,[],[f479]) ).
cnf(s31,plain,
~ spl0_21,
inference(sat_conversion,[],[f518]) ).
cnf(s35,plain,
spl0_18,
inference(rat,[],[s25,s31,s27]) ).
cnf(s36,plain,
~ spl0_8,
inference(rat,[],[s21,s35]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s5,s36,s8]) ).
fof(f534,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:19:48 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.43/1.23 % (3729708)Input is clausal, will run a generic CNF schedule.
% 2.43/1.23 % (3729756)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=182087441:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.43/1.23 % (3729756)First to succeed.
% 2.43/1.23 % (3729756)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3729708"
% 2.43/1.23 % (3729758)dis-21_1_sil=8000:lcm=predicate:random_seed=1851016860: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)
% 2.43/1.23 % (3729755)lrs+10_1_sil=8000:sp=occurrence:random_seed=3119798387:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.43/1.23 % (3729753)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3405576829:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.43/1.23 % (3729752)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=2547098334:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.43/1.23 % (3729754)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2776754958:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.43/1.23 % (3729755)Refutation not found, incomplete strategy
% 2.43/1.23 % (3729755)------------------------------
% 2.43/1.23 % (3729755)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.23 % (3729755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.23 % (3729755)CaDiCaL version: 2.1.3
% 2.43/1.23 % (3729755)Termination reason: Refutation not found, incomplete strategy
% 2.43/1.23 % (3729755)Time elapsed: 0.0000 s
% 2.43/1.23 % (3729755)Peak memory usage: 86 MB
% 2.43/1.23 % (3729757)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=70155405:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.43/1.23 % (3729757)Also succeeded, but the first one will report.
% 2.43/1.23 % (3729758)Instruction limit reached!
% 2.43/1.23 % (3729758)------------------------------
% 2.43/1.23 % (3729758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.23 % (3729758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.23 % (3729758)CaDiCaL version: 2.1.3
% 2.43/1.23 % (3729758)Termination reason: Instruction limit
% 2.43/1.23 % (3729758)Termination phase: Saturation
% 2.43/1.23 % (3729758)Time elapsed: 0.070 s
% 2.43/1.23 % (3729758)Peak memory usage: 89 MB
% 2.43/1.23 % (3729758)Instructions burned: 118 (million)
% 2.43/1.23 % (3729756)Refutation found. Thanks to Tanya!
% 2.43/1.23 % SZS status Unsatisfiable for theBenchmark
% 2.43/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/1.23 % (3729756)------------------------------
% 2.43/1.23 % (3729756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.43/1.23 % (3729756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/1.23 % (3729756)CaDiCaL version: 2.1.3
% 2.43/1.23 % (3729756)Termination reason: Refutation
% 2.43/1.23 % (3729756)Time elapsed: 0.006 s
% 2.43/1.23 % (3729756)Peak memory usage: 89 MB
% 2.43/1.23 % (3729756)Instructions burned: 15 (million)
% 2.43/1.23 % (3729756)------------------------------
% 2.43/1.23 % (3729756)------------------------------
% 2.43/1.23 % (3729708)Success in time 0.274 s
% 2.43/1.23 % Vampire exiting
%------------------------------------------------------------------------------