%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP123-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 10:16:42 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 15 unt; 2 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 65 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 28 ( 0 sgn 28 !; 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(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
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(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(f16,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(f37,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X2,X1)
| ~ product(X0,X2,X3)
| ~ product(X0,X0,X1)
| equalish(X2,X0) ),
inference(resolution,[],[f14,f16]) ).
fof(f62,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f13,f14]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ product(X2,X2,e_3)
| product(X1,X0,e_1)
| product(X1,X0,e_2)
| ~ group_element(X1)
| ~ product(X2,X0,X1)
| ~ group_element(X0)
| equalish(X0,X2) ),
inference(resolution,[],[f10,f37]) ).
fof(f99,plain,
! [X0,X1] :
( ~ product(e_3,X1,X0)
| product(X0,X1,e_2)
| ~ group_element(X0)
| product(X0,X1,e_1)
| ~ group_element(X1)
| equalish(X1,e_3) ),
inference(resolution,[],[f81,f14]) ).
fof(f113,plain,
! [X0] :
( product(e_3,X0,e_2)
| ~ group_element(e_3)
| product(e_3,X0,e_1)
| ~ group_element(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,[],[f99,f10]) ).
fof(f114,plain,
! [X0] :
( product(e_3,X0,e_2)
| ~ group_element(e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(X0,e_3) ),
inference(duplicate_literal_removal,[],[f113]) ).
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,[],[f114,f3]) ).
fof(f141,plain,
( product(e_3,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[],[f116,f62]) ).
fof(f146,plain,
( product(e_3,e_2,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f141,f2]) ).
fof(f148,plain,
( product(e_3,e_2,e_1)
| equalish(e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f146,f7]) ).
fof(f149,plain,
product(e_3,e_2,e_1),
inference(forward_subsumption_resolution,[],[f148,f9]) ).
fof(f184,plain,
( product(e_1,e_2,e_2)
| ~ group_element(e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3) ),
inference(resolution,[],[f149,f99]) ).
fof(f187,plain,
! [X0] :
( ~ product(X0,e_2,e_1)
| equalish(X0,e_3) ),
inference(resolution,[],[f149,f13]) ).
fof(f192,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| equalish(e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f184,f1]) ).
fof(f193,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f192,f2]) ).
fof(f194,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(forward_subsumption_resolution,[],[f193,f7]) ).
fof(f232,definition,
( spl0_20
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f234,plain,
( product(e_1,e_2,e_1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl0_21
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f238,plain,
( product(e_1,e_2,e_2)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,plain,
( spl0_20
| spl0_21 ),
inference(avatar_split_clause,[],[f194,f236,f232]) ).
fof(f240,plain,
( equalish(e_1,e_3)
| ~ spl0_20 ),
inference(resolution,[],[f234,f187]) ).
fof(f251,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f240,f5]) ).
fof(f252,plain,
~ spl0_20,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f260,plain,
( equalish(e_1,e_2)
| ~ spl0_21 ),
inference(resolution,[],[f238,f62]) ).
fof(f262,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f260,f4]) ).
fof(f263,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[],[f262]) ).
cnf(s168,plain,
( spl0_20
| spl0_21 ),
inference(sat_conversion,[],[f239]) ).
cnf(s177,plain,
~ spl0_20,
inference(sat_conversion,[],[f252]) ).
cnf(s182,plain,
~ spl0_21,
inference(sat_conversion,[],[f263]) ).
cnf(s189,plain,
$false,
inference(rat,[],[s168,s182,s177]) ).
fof(f264,plain,
$false,
inference(avatar_sat_refutation,[],[s189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:21:56 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.44 % (242746)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (242753)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=615466329:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (242753) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-242746-242753"...
% 0.10/0.44 % (242753)...printing done.
% 0.10/0.44 % (242752)% WARNING: option uhcvi not known.
% 0.10/0.44 % (242753)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (242753)------------------------------
% 0.10/0.45 % (242753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (242753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (242753)CaDiCaL version: 2.1.3
% 0.10/0.45 % (242753)Termination reason: Refutation
% 0.10/0.45 % (242753)Time elapsed: 0.003 s
% 0.10/0.45 % (242753)Peak memory usage: 12 MB
% 0.10/0.45 % (242753)Instructions burned: 7 (million)
% 0.10/0.45 % (242746)Success in time 0.029 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------