%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP123-2.003 : 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 : n007.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 10:16:43 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 51 ( 16 unt; 3 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 52 ~; 51 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f8,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f9,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f11,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f12,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f14,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f15,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f16,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f20,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f21,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_3)
| ~ product(e_1,X3,X1) ),
inference(resolution,[],[f11,f21]) ).
fof(f45,plain,
! [X0,X1] :
( ~ product(X0,X1,e_1)
| ~ product(X0,e_3,e_3)
| ~ product(e_1,X1,e_3) ),
inference(resolution,[],[f20,f26]) ).
fof(f50,definition,
( spl0_1
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f51,plain,
( product(e_3,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f52,plain,
( ~ product(e_3,e_2,e_2)
| spl0_1 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f72,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[],[f18,f15]) ).
fof(f75,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f19,f12]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[],[f19,f14]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[],[f19,f15]) ).
fof(f80,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| product(e_1,X0,e_3) ),
inference(resolution,[],[f16,f7]) ).
fof(f82,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3) ),
inference(resolution,[],[f16,f9]) ).
fof(f101,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[],[f72,f20]) ).
fof(f103,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[],[f75,f20]) ).
fof(f105,plain,
! [X0] :
( ~ product(e_3,X0,e_1)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[],[f45,f20]) ).
fof(f108,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(resolution,[],[f80,f8]) ).
fof(f111,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(forward_subsumption_resolution,[],[f108,f103]) ).
fof(f122,definition,
( spl0_5
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f124,plain,
( product(e_1,e_2,e_3)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f126,definition,
( spl0_6
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f129,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f111,f126,f122]) ).
fof(f156,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(resolution,[],[f82,f8]) ).
fof(f158,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_3)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f156,f52]) ).
fof(f160,plain,
( product(e_3,e_2,e_1)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f158,f101]) ).
fof(f170,plain,
( ~ product(e_1,e_2,e_3)
| spl0_1 ),
inference(resolution,[],[f160,f105]) ).
fof(f176,plain,
( ~ product(e_1,e_2,e_1)
| spl0_1 ),
inference(resolution,[],[f160,f77]) ).
fof(f186,plain,
( ~ spl0_6
| spl0_1 ),
inference(avatar_split_clause,[],[f176,f50,f126]) ).
fof(f189,plain,
( $false
| spl0_1
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f170,f124]) ).
fof(f190,plain,
( spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f200,plain,
( ~ product(e_2,e_2,e_2)
| ~ spl0_1 ),
inference(resolution,[],[f51,f78]) ).
fof(f211,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f200,f20]) ).
fof(f212,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f211]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f129]) ).
cnf(s10,plain,
( spl0_1
| ~ spl0_6 ),
inference(sat_conversion,[],[f186]) ).
cnf(s12,plain,
( spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f190]) ).
cnf(s14,plain,
~ spl0_1,
inference(sat_conversion,[],[f212]) ).
cnf(s15,plain,
~ spl0_5,
inference(rat,[],[s12,s14]) ).
cnf(s16,plain,
~ spl0_6,
inference(rat,[],[s10,s14]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s4,s16,s15]) ).
fof(f213,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:17:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 0.10/0.45 % (1151815)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1151824)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1427454788:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (1151824) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1151815-1151824"...
% 0.10/0.45 % (1151821)% WARNING: option uhcvi not known.
% 0.10/0.45 % (1151824)...printing done.
% 0.10/0.45 % (1151824)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1151824)------------------------------
% 0.10/0.45 % (1151824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1151824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1151824)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1151824)Termination reason: Refutation
% 0.10/0.45 % (1151824)Time elapsed: 0.003 s
% 0.10/0.45 % (1151824)Peak memory usage: 12 MB
% 0.10/0.45 % (1151824)Instructions burned: 7 (million)
% 0.10/0.45 % (1151815)Success in time 0.029 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------