%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP125-1.003 : 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 : n019.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 10:12:43 AM UTC 2026
% Result : Unsatisfiable 0.14s 1.30s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 14 unt; 1 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 55 ~; 58 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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] :
( 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(f11,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X2)
| ~ product(X0,X1,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f13,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(f14,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f15,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
fof(f17,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f11,f14]) ).
fof(f24,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f12,f14]) ).
fof(f31,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X4,X2,X1)
| equalish(X0,X3)
| ~ product(X0,X1,X2)
| ~ product(X2,X4,X3) ),
inference(resolution,[],[f13,f15]) ).
fof(f32,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f13,f14]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| equalish(X0,X2)
| ~ product(X0,X1,X1) ),
inference(factoring,[],[f31]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ product(X2,X0,X1)
| equalish(X0,X1)
| ~ product(X0,X2,X1) ),
inference(resolution,[],[f17,f15]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ product(X2,X1,X0)
| equalish(X0,X1)
| ~ product(X1,X2,X1) ),
inference(resolution,[],[f24,f15]) ).
fof(f63,plain,
! [X0] :
( equalish(X0,e_3)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| ~ group_element(e_3) ),
inference(resolution,[],[f24,f10]) ).
fof(f65,plain,
! [X0] :
( product(e_3,X0,e_2)
| ~ group_element(X0)
| product(e_3,X0,e_1)
| equalish(X0,e_3) ),
inference(forward_subsumption_resolution,[],[f63,f3]) ).
fof(f756,plain,
( ~ group_element(e_2)
| product(e_3,e_2,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[],[f65,f32]) ).
fof(f762,plain,
( product(e_3,e_2,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f756,f2]) ).
fof(f775,plain,
( product(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f762,f7]) ).
fof(f777,plain,
product(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f775,f9]) ).
fof(f782,definition,
( spl0_5
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f783,plain,
( product(e_3,e_2,e_1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f785,plain,
spl0_5,
inference(avatar_split_clause,[],[f777,f782]) ).
fof(f831,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_3,e_3)
| ~ spl0_5 ),
inference(resolution,[],[f783,f47]) ).
fof(f833,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ spl0_5 ),
inference(resolution,[],[f783,f54]) ).
fof(f834,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_3,e_2)
| ~ spl0_5 ),
inference(resolution,[],[f783,f62]) ).
fof(f837,plain,
( ~ product(e_2,e_3,e_2)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f834,f4]) ).
fof(f838,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f833,f6]) ).
fof(f840,plain,
( ~ product(e_2,e_3,e_3)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f831,f6]) ).
fof(f1118,plain,
( ~ group_element(e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| ~ spl0_5 ),
inference(resolution,[],[f840,f10]) ).
fof(f1120,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| ~ group_element(e_2)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1118,f3]) ).
fof(f1121,plain,
( product(e_2,e_3,e_2)
| ~ group_element(e_2)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1120,f838]) ).
fof(f1122,plain,
( ~ group_element(e_2)
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1121,f837]) ).
fof(f1123,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f1122,f2]) ).
fof(f1124,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f1123]) ).
cnf(s4,plain,
spl0_5,
inference(sat_conversion,[],[f785]) ).
cnf(s25,plain,
~ spl0_5,
inference(sat_conversion,[],[f1124]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s4,s25]) ).
fof(f1125,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 09:23:30 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.14/1.30 % (2829697)Input is clausal, will run a generic CNF schedule.
% 0.14/1.30 % (2829706)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3942315865:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.14/1.30 % (2829706)First to succeed.
% 0.14/1.30 % (2829706)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2829697"
% 0.14/1.30 % (2829707)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2815632068:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.14/1.30 % (2829708)dis-21_1_sil=8000:lcm=predicate:random_seed=1676045431: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)
% 0.14/1.30 % (2829705)lrs+10_1_sil=8000:sp=occurrence:random_seed=1072531183:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.14/1.30 % (2829703)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1345697554:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.14/1.30 % (2829702)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=3767551482:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.14/1.30 % (2829704)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4138394826:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.14/1.30 % (2829707)Also succeeded, but the first one will report.
% 0.14/1.30 % (2829705)Also succeeded, but the first one will report.
% 0.14/1.30 % (2829708)Also succeeded, but the first one will report.
% 0.14/1.30 % (2829706)Refutation found. Thanks to Tanya!
% 0.14/1.30 % SZS status Unsatisfiable for theBenchmark
% 0.14/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.30 % (2829706)------------------------------
% 0.14/1.30 % (2829706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.30 % (2829706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.30 % (2829706)CaDiCaL version: 2.1.3
% 0.14/1.30 % (2829706)Termination reason: Refutation
% 0.14/1.30 % (2829706)Time elapsed: 0.016 s
% 0.14/1.30 % (2829706)Peak memory usage: 89 MB
% 0.14/1.30 % (2829706)Instructions burned: 56 (million)
% 0.14/1.30 % (2829706)------------------------------
% 0.14/1.30 % (2829706)------------------------------
% 0.14/1.30 % (2829697)Success in time 0.283 s
% 0.14/1.30 % Vampire exiting
%------------------------------------------------------------------------------