%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP123-6.003 : 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 : n026.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 10:12:40 AM UTC 2026
% Result : Unsatisfiable 2.55s 1.33s
% Output : Refutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 54 ( 21 unt; 4 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 49 ~; 61 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f6,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f10,axiom,
! [X0,X1] :
( product1(X0,X1,e_3)
| ~ group_element(X1)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f14,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f19,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2)
| product2(X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f25,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f12,f14]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product1(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f13,f14]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product2(X0,X0,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f16,f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ product1(X2,X0,X1)
| product1(X1,X0,e_1)
| product1(X1,X0,e_2)
| ~ group_element(X1)
| ~ group_element(X0)
| product2(e_3,X2,X0) ),
inference(resolution,[],[f10,f20]) ).
fof(f40,plain,
! [X0] :
( ~ group_element(X0)
| product1(e_3,X0,e_1)
| product1(e_3,X0,e_2)
| ~ group_element(e_3)
| equalish(X0,e_3) ),
inference(resolution,[],[f10,f25]) ).
fof(f43,plain,
! [X0] :
( product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3) ),
inference(forward_subsumption_resolution,[],[f40,f3]) ).
fof(f261,plain,
( product1(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[],[f43,f26]) ).
fof(f274,plain,
( product1(e_3,e_2,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f261,f2]) ).
fof(f277,plain,
( product1(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f274,f7]) ).
fof(f284,definition,
( spl0_14
<=> product1(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f286,plain,
( product1(e_3,e_2,e_1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f288,plain,
product1(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f277,f9]) ).
fof(f289,plain,
spl0_14,
inference(avatar_split_clause,[],[f288,f284]) ).
fof(f291,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ group_element(e_1)
| ~ group_element(e_2)
| product2(e_3,e_3,e_2)
| ~ spl0_14 ),
inference(resolution,[],[f286,f37]) ).
fof(f296,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| ~ group_element(e_2)
| product2(e_3,e_3,e_2)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f291,f1]) ).
fof(f297,plain,
( product1(e_1,e_2,e_1)
| product1(e_1,e_2,e_2)
| product2(e_3,e_3,e_2)
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f296,f2]) ).
fof(f299,definition,
( spl0_15
<=> product2(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f301,plain,
( product2(e_3,e_3,e_2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f303,definition,
( spl0_16
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f305,plain,
( product1(e_1,e_2,e_2)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f307,definition,
( spl0_17
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f309,plain,
( product1(e_1,e_2,e_1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f310,plain,
( spl0_15
| spl0_16
| spl0_17
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f297,f284,f307,f303,f299]) ).
fof(f324,plain,
( equalish(e_2,e_3)
| ~ spl0_15 ),
inference(resolution,[],[f301,f28]) ).
fof(f326,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f324,f7]) ).
fof(f327,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f348,plain,
( equalish(e_1,e_2)
| ~ spl0_16 ),
inference(resolution,[],[f305,f26]) ).
fof(f357,plain,
( $false
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f348,f4]) ).
fof(f358,plain,
~ spl0_16,
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f383,plain,
( equalish(e_2,e_1)
| ~ spl0_17 ),
inference(resolution,[],[f309,f25]) ).
fof(f390,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f383,f6]) ).
fof(f391,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f390]) ).
cnf(s12,plain,
spl0_14,
inference(sat_conversion,[],[f289]) ).
cnf(s13,plain,
( ~ spl0_14
| spl0_15
| spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f310]) ).
cnf(s14,plain,
~ spl0_15,
inference(sat_conversion,[],[f327]) ).
cnf(s15,plain,
~ spl0_16,
inference(sat_conversion,[],[f358]) ).
cnf(s16,plain,
~ spl0_17,
inference(sat_conversion,[],[f391]) ).
cnf(s17,plain,
~ spl0_14,
inference(rat,[],[s13,s16,s15,s14]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s12,s17]) ).
fof(f392,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n026.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 09:23:26 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
% 2.55/1.33 % (2569469)Input is clausal, will run a generic CNF schedule.
% 2.55/1.33 % (2569477)lrs+10_1_sil=8000:sp=occurrence:random_seed=145165054:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.55/1.33 % (2569477)First to succeed.
% 2.55/1.33 % (2569477)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2569469"
% 2.55/1.33 % (2569475)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2663151684:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.55/1.33 % (2569478)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1596700633:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.55/1.33 % (2569476)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3672404274:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.55/1.33 % (2569479)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2221713599:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.55/1.33 % (2569480)dis-21_1_sil=8000:lcm=predicate:random_seed=532712769: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)
% 2.55/1.33 % (2569474)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=249085800:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.55/1.33 % (2569478)Also succeeded, but the first one will report.
% 2.55/1.33 % (2569480)Also succeeded, but the first one will report.
% 2.55/1.33 % (2569479)Also succeeded, but the first one will report.
% 2.55/1.33 % (2569477)Refutation found. Thanks to Tanya!
% 2.55/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.55/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.55/1.33 % (2569477)------------------------------
% 2.55/1.33 % (2569477)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.33 % (2569477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.33 % (2569477)CaDiCaL version: 2.1.3
% 2.55/1.33 % (2569477)Termination reason: Refutation
% 2.55/1.33 % (2569477)Time elapsed: 0.005 s
% 2.55/1.33 % (2569477)Peak memory usage: 89 MB
% 2.55/1.33 % (2569477)Instructions burned: 11 (million)
% 2.55/1.33 % (2569477)------------------------------
% 2.55/1.33 % (2569477)------------------------------
% 2.55/1.33 % (2569469)Success in time 0.271 s
% 2.55/1.33 % Vampire exiting
%------------------------------------------------------------------------------