%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n009.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 10:16:44 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 20
% Syntax : Number of formulae : 63 ( 21 unt; 6 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 117 ( 54 ~; 57 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 11 ( 10 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,
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(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(f8,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
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] :
( ~ group_element(X0)
| ~ group_element(X1)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| product1(X0,X1,e_3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X0,X1,X2)
| ~ product1(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ product1(X0,X1,X2)
| ~ product1(X3,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,X2)
| ~ product2(X0,X1,X3)
| 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(X0,X1,X2)
| ~ product1(X2,X1,X3)
| product2(X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
fof(f25,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f12,f14]) ).
fof(f26,plain,
! [X0,X1] :
( ~ product1(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f13,f14]) ).
fof(f28,plain,
! [X0,X1] :
( ~ product2(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f16,f19]) ).
fof(f34,plain,
! [X0] :
( ~ group_element(X0)
| product1(e_1,X0,e_1)
| product1(e_1,X0,e_2)
| product1(e_1,X0,e_3) ),
inference(resolution,[],[f10,f1]) ).
fof(f35,plain,
! [X0] :
( ~ group_element(X0)
| product1(e_2,X0,e_1)
| product1(e_2,X0,e_2)
| product1(e_2,X0,e_3) ),
inference(resolution,[],[f10,f2]) ).
fof(f43,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3) ),
inference(resolution,[],[f34,f3]) ).
fof(f45,definition,
( spl0_1
<=> product1(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f47,plain,
( product1(e_1,e_3,e_3)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f49,definition,
( spl0_2
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f51,plain,
( product1(e_1,e_3,e_2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f53,definition,
( spl0_3
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f55,plain,
( product1(e_1,e_3,e_1)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f56,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f43,f53,f49,f45]) ).
fof(f72,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3) ),
inference(resolution,[],[f35,f3]) ).
fof(f74,definition,
( spl0_7
<=> product1(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f76,plain,
( product1(e_2,e_3,e_3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_8
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f80,plain,
( product1(e_2,e_3,e_2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_9
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f84,plain,
( product1(e_2,e_3,e_1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(avatar_split_clause,[],[f72,f82,f78,f74]) ).
fof(f102,plain,
( ! [X0] :
( ~ product1(e_2,e_3,X0)
| product2(X0,e_1,e_3) )
| ~ spl0_2 ),
inference(resolution,[],[f51,f20]) ).
fof(f228,plain,
( equalish(e_3,e_2)
| ~ spl0_7 ),
inference(resolution,[],[f76,f26]) ).
fof(f229,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f228,f9]) ).
fof(f230,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f236,plain,
( equalish(e_2,e_3)
| ~ spl0_8 ),
inference(resolution,[],[f80,f25]) ).
fof(f237,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f236,f7]) ).
fof(f238,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f237]) ).
fof(f239,plain,
( product2(e_1,e_1,e_3)
| ~ spl0_2
| ~ spl0_9 ),
inference(resolution,[],[f84,f102]) ).
fof(f251,plain,
( equalish(e_1,e_3)
| ~ spl0_2
| ~ spl0_9 ),
inference(resolution,[],[f239,f28]) ).
fof(f252,plain,
( $false
| ~ spl0_2
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f251,f5]) ).
fof(f253,plain,
( ~ spl0_2
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f259,plain,
( equalish(e_1,e_3)
| ~ spl0_3 ),
inference(resolution,[],[f55,f25]) ).
fof(f260,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f259,f5]) ).
fof(f261,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f267,plain,
( equalish(e_3,e_1)
| ~ spl0_1 ),
inference(resolution,[],[f47,f26]) ).
fof(f268,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f267,f8]) ).
fof(f269,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f268]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
( spl0_7
| spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f85]) ).
cnf(s13,plain,
~ spl0_7,
inference(sat_conversion,[],[f230]) ).
cnf(s14,plain,
~ spl0_8,
inference(sat_conversion,[],[f238]) ).
cnf(s15,plain,
( ~ spl0_2
| ~ spl0_9 ),
inference(sat_conversion,[],[f253]) ).
cnf(s16,plain,
~ spl0_3,
inference(sat_conversion,[],[f261]) ).
cnf(s17,plain,
~ spl0_1,
inference(sat_conversion,[],[f269]) ).
cnf(s18,plain,
spl0_9,
inference(rat,[],[s3,s14,s13]) ).
cnf(s19,plain,
~ spl0_2,
inference(rat,[],[s15,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s16,s19,s17]) ).
fof(f270,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.10/0.39 % Computer : n009.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:20:31 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 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
% 0.18/0.46 % (1764650)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (1764660)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1828158950:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.46 % (1764660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1764650-1764660"...
% 0.18/0.46 % (1764656)% WARNING: option uhcvi not known.
% 0.18/0.46 % (1764660)...printing done.
% 0.18/0.46 % (1764660)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (1764660)------------------------------
% 0.18/0.46 % (1764660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (1764660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (1764660)CaDiCaL version: 2.1.3
% 0.18/0.46 % (1764660)Termination reason: Refutation
% 0.18/0.46 % (1764660)Time elapsed: 0.002 s
% 0.18/0.46 % (1764660)Peak memory usage: 12 MB
% 0.18/0.46 % (1764660)Instructions burned: 4 (million)
% 0.18/0.46 % (1764650)Success in time 0.027 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------