%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 10:16:53 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 103 ( 23 unt; 11 def)
% Number of atoms : 278 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 289 ( 114 ~; 164 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f4,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f5,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f10,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X3,X4,X2)
| ~ product(X5,X1,X0)
| ~ product(X5,X4,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
fof(f11,plain,
~ group_element(e_1),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f12,plain,
~ group_element(e_2),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f13,plain,
equalish(e_1,e_2),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f14,plain,
equalish(e_2,e_1),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( group_element(X1)
| group_element(X0)
| ~ product(X0,X1,e_1)
| ~ product(X0,X1,e_2) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f17,plain,
! [X2,X3,X0,X1] :
( product(X0,X3,X2)
| product(X0,X1,X2)
| ~ equalish(X1,X3) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( product(X3,X1,X2)
| product(X0,X1,X2)
| ~ equalish(X0,X3) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f20,plain,
! [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) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f21,plain,
! [X0] :
( ~ product(X0,e_1,e_2)
| ~ product(X0,e_1,e_1)
| group_element(X0) ),
inference(resolution,[],[f15,f11]) ).
fof(f22,plain,
! [X0] :
( ~ product(X0,e_2,e_2)
| ~ product(X0,e_2,e_1)
| group_element(X0) ),
inference(resolution,[],[f15,f12]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( product(e_2,e_1,X1)
| group_element(X0)
| ~ product(X0,e_1,e_1)
| product(X0,X2,X3)
| product(X3,X2,X1)
| ~ equalish(X2,e_1) ),
inference(resolution,[],[f21,f20]) ).
fof(f28,plain,
! [X2,X0,X1] :
( group_element(X0)
| ~ product(X0,e_1,e_1)
| product(X0,X1,X2)
| product(X2,X1,e_2)
| ~ equalish(X1,e_1)
| ~ product(e_2,e_1,e_1)
| group_element(e_2) ),
inference(resolution,[],[f26,f21]) ).
fof(f30,definition,
( spl0_1
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f32,plain,
( group_element(e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f34,definition,
( spl0_2
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f36,plain,
( ~ product(e_2,e_1,e_1)
| spl0_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl0_3
<=> ! [X2,X0,X1] :
( group_element(X0)
| ~ equalish(X1,e_1)
| product(X2,X1,e_2)
| product(X0,X1,X2)
| ~ product(X0,e_1,e_1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f39,plain,
( ! [X2,X0,X1] :
( group_element(X0)
| ~ equalish(X1,e_1)
| product(X2,X1,e_2)
| product(X0,X1,X2)
| ~ product(X0,e_1,e_1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f28,f38,f34,f30]) ).
fof(f42,plain,
( ! [X0] :
( product(X0,e_1,e_1)
| ~ equalish(X0,e_2) )
| spl0_2 ),
inference(resolution,[],[f36,f18]) ).
fof(f45,plain,
( ! [X2,X0,X1] :
( product(e_1,e_1,X0)
| product(e_2,X1,X2)
| product(X2,X1,X0)
| ~ equalish(X1,e_1) )
| spl0_2 ),
inference(resolution,[],[f36,f20]) ).
fof(f56,plain,
( ! [X0,X1] :
( product(e_2,X0,X1)
| product(X1,X0,e_2)
| ~ equalish(X0,e_1)
| ~ product(e_1,e_1,e_1)
| group_element(e_1) )
| spl0_2 ),
inference(resolution,[],[f45,f21]) ).
fof(f58,definition,
( spl0_4
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f60,plain,
( group_element(e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f62,definition,
( spl0_5
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f64,plain,
( ~ product(e_1,e_1,e_1)
| spl0_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f66,definition,
( spl0_6
<=> ! [X0,X1] :
( product(e_2,X0,X1)
| ~ equalish(X0,e_1)
| product(X1,X0,e_2) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f67,plain,
( ! [X0,X1] :
( product(e_2,X0,X1)
| ~ equalish(X0,e_1)
| product(X1,X0,e_2) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f68,plain,
( spl0_4
| ~ spl0_5
| spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f56,f34,f66,f62,f58]) ).
fof(f70,plain,
( ~ equalish(e_1,e_2)
| spl0_2
| spl0_5 ),
inference(resolution,[],[f64,f42]) ).
fof(f76,plain,
( $false
| spl0_2
| spl0_5 ),
inference(resolution,[],[f70,f13]) ).
fof(f77,plain,
( spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f78,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f60,f11]) ).
fof(f79,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f81,plain,
( ! [X0,X1] :
( ~ equalish(X0,e_1)
| product(X1,X0,e_2)
| product(e_2,X0,X1)
| ~ product(e_2,e_1,e_1) )
| ~ spl0_3 ),
inference(resolution,[],[f39,f12]) ).
fof(f82,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f81,f38,f66,f34]) ).
fof(f97,plain,
( ~ equalish(e_2,e_1)
| product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| group_element(e_2)
| ~ spl0_6 ),
inference(resolution,[],[f67,f22]) ).
fof(f99,definition,
( spl0_8
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f101,plain,
( ~ product(e_2,e_2,e_1)
| spl0_8 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f103,definition,
( spl0_9
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f104,plain,
( ~ product(e_2,e_2,e_2)
| spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f105,plain,
( product(e_2,e_2,e_2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,definition,
( spl0_10
<=> equalish(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f109,plain,
( ~ equalish(e_2,e_1)
| spl0_10 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_1
| ~ spl0_8
| spl0_9
| ~ spl0_10
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f97,f66,f107,f103,f99,f30]) ).
fof(f111,plain,
( $false
| spl0_10 ),
inference(resolution,[],[f109,f14]) ).
fof(f112,plain,
spl0_10,
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f113,plain,
( ~ equalish(e_2,e_1)
| product(e_1,e_2,e_2)
| ~ spl0_6
| spl0_8 ),
inference(resolution,[],[f101,f67]) ).
fof(f120,definition,
( spl0_11
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f122,plain,
( product(e_1,e_2,e_2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_11
| ~ spl0_10
| ~ spl0_6
| spl0_8 ),
inference(avatar_split_clause,[],[f113,f99,f66,f107,f120]) ).
fof(f129,plain,
( ! [X0] :
( product(e_2,X0,e_1)
| ~ equalish(X0,e_1) )
| spl0_2 ),
inference(resolution,[],[f36,f17]) ).
fof(f133,plain,
( ~ equalish(e_2,e_1)
| product(e_2,e_2,e_2)
| ~ spl0_6
| spl0_9 ),
inference(resolution,[],[f104,f67]) ).
fof(f139,plain,
( ~ product(e_1,e_2,e_1)
| group_element(e_1)
| ~ spl0_11 ),
inference(resolution,[],[f122,f22]) ).
fof(f141,definition,
( spl0_12
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f143,plain,
( ~ product(e_1,e_2,e_1)
| spl0_12 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_4
| ~ spl0_12
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f139,f120,f141,f58]) ).
fof(f152,plain,
( ~ equalish(e_2,e_1)
| spl0_2
| spl0_8 ),
inference(resolution,[],[f129,f101]) ).
fof(f153,plain,
( ~ spl0_10
| spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f152,f99,f34,f107]) ).
fof(f154,plain,
( spl0_9
| ~ spl0_10
| ~ spl0_6
| spl0_9 ),
inference(avatar_split_clause,[],[f133,f103,f66,f107,f103]) ).
fof(f155,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f32,f12]) ).
fof(f156,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f157,plain,
( ~ product(e_2,e_2,e_1)
| group_element(e_2)
| ~ spl0_9 ),
inference(resolution,[],[f105,f22]) ).
fof(f158,plain,
( spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f157,f103,f99,f30]) ).
fof(f164,plain,
( ! [X0] :
( product(X0,e_2,e_1)
| ~ equalish(X0,e_2) )
| spl0_8 ),
inference(resolution,[],[f101,f18]) ).
fof(f169,plain,
( ~ equalish(e_1,e_2)
| spl0_8
| spl0_12 ),
inference(resolution,[],[f164,f143]) ).
fof(f171,plain,
( $false
| spl0_8
| spl0_12 ),
inference(resolution,[],[f169,f13]) ).
fof(f172,plain,
( spl0_8
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f171]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( spl0_2
| spl0_4
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f68]) ).
cnf(s3,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f77]) ).
cnf(s4,plain,
~ spl0_4,
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f82]) ).
cnf(s7,plain,
( spl0_1
| ~ spl0_6
| ~ spl0_8
| spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f110]) ).
cnf(s8,plain,
spl0_10,
inference(sat_conversion,[],[f112]) ).
cnf(s9,plain,
( ~ spl0_6
| spl0_8
| ~ spl0_10
| spl0_11 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f144]) ).
cnf(s11,plain,
( spl0_2
| spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f153]) ).
cnf(s12,plain,
( spl0_9
| ~ spl0_6
| spl0_9
| ~ spl0_10 ),
inference(sat_conversion,[],[f154]) ).
cnf(s13,plain,
( ~ spl0_6
| spl0_9
| ~ spl0_10 ),
inference(rat,[],[s12]) ).
cnf(s14,plain,
~ spl0_1,
inference(sat_conversion,[],[f156]) ).
cnf(s15,plain,
( spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f158]) ).
cnf(s17,plain,
( spl0_8
| spl0_12 ),
inference(sat_conversion,[],[f172]) ).
cnf(s18,plain,
( ~ spl0_6
| ~ spl0_8
| spl0_9 ),
inference(rat,[],[s7,s8,s14]) ).
cnf(s19,plain,
( spl0_2
| ~ spl0_5
| spl0_6 ),
inference(rat,[],[s2,s4]) ).
cnf(s20,plain,
( ~ spl0_2
| spl0_3 ),
inference(rat,[],[s1,s14]) ).
cnf(s21,plain,
spl0_2,
inference(rat,[],[s19,s18,s15,s3,s11,s14,s8]) ).
cnf(s23,plain,
spl0_3,
inference(rat,[],[s20,s21]) ).
cnf(s24,plain,
spl0_6,
inference(rat,[],[s5,s21,s23]) ).
cnf(s25,plain,
spl0_9,
inference(rat,[],[s13,s8,s24]) ).
cnf(s26,plain,
~ spl0_8,
inference(rat,[],[s15,s14,s25]) ).
cnf(s27,plain,
spl0_12,
inference(rat,[],[s17,s26]) ).
cnf(s28,plain,
spl0_11,
inference(rat,[],[s9,s24,s8,s26]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s10,s4,s27,s28]) ).
fof(f173,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 09:31:45 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.46 % (1398285)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (1398296)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=489980957:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.46 % (1398296) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1398285-1398296"...
% 0.17/0.46 % (1398291)% WARNING: option uhcvi not known.
% 0.17/0.46 % (1398296)...printing done.
% 0.17/0.46 % (1398296)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1398296)------------------------------
% 0.17/0.47 % (1398296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1398296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1398296)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1398296)Termination reason: Refutation
% 0.17/0.47 % (1398296)Time elapsed: 0.003 s
% 0.17/0.47 % (1398296)Peak memory usage: 12 MB
% 0.17/0.47 % (1398296)Instructions burned: 6 (million)
% 0.17/0.47 % (1398285)Success in time 0.031 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------