%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP127-1.004 : 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 : n018.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 10:16:49 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 53
% Syntax : Number of formulae : 247 ( 62 unt; 32 def)
% Number of atoms : 540 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 520 ( 227 ~; 261 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 36 ( 35 usr; 33 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn 32 !; 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,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f8,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f11,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f12,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f14,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f15,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f16,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f17,axiom,
! [X0,X1] :
( ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| product(X0,X1,e_4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f19,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(f20,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(f21,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product(X2,X0,X3)
| ~ product(X0,X1,X2)
| product(X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
fof(f26,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X1,X0) ),
inference(resolution,[],[f19,f21]) ).
fof(f27,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f20,f21]) ).
fof(f29,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_1,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_3)
| product(X0,e_1,e_4) ),
inference(resolution,[],[f17,f1]) ).
fof(f30,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_2,e_1)
| product(X0,e_2,e_2)
| product(X0,e_2,e_3)
| product(X0,e_2,e_4) ),
inference(resolution,[],[f17,f2]) ).
fof(f31,plain,
! [X0] :
( ~ group_element(X0)
| product(X0,e_3,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_3)
| product(X0,e_3,e_4) ),
inference(resolution,[],[f17,f3]) ).
fof(f36,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(resolution,[],[f29,f2]) ).
fof(f38,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(resolution,[],[f29,f4]) ).
fof(f40,definition,
( spl0_1
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f42,plain,
( product(e_4,e_1,e_4)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f44,definition,
( spl0_2
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f46,plain,
( product(e_4,e_1,e_3)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl0_3
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f50,plain,
( product(e_4,e_1,e_2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl0_4
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f54,plain,
( product(e_4,e_1,e_1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f38,f52,f48,f44,f40]) ).
fof(f61,definition,
( spl0_6
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f62,plain,
( ~ product(e_3,e_1,e_3)
| spl0_6 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( product(e_3,e_1,e_3)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f65,definition,
( spl0_7
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f67,plain,
( product(e_3,e_1,e_2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f74,definition,
( spl0_9
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f76,plain,
( product(e_2,e_1,e_4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl0_10
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f80,plain,
( product(e_2,e_1,e_3)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_11
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f83,plain,
( ~ product(e_2,e_1,e_2)
| spl0_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( product(e_2,e_1,e_2)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f86,definition,
( spl0_12
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f88,plain,
( product(e_2,e_1,e_1)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f89,plain,
( spl0_9
| spl0_10
| spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f36,f86,f82,f78,f74]) ).
fof(f90,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(resolution,[],[f30,f1]) ).
fof(f92,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(resolution,[],[f30,f3]) ).
fof(f93,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(resolution,[],[f30,f4]) ).
fof(f95,definition,
( spl0_13
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f97,plain,
( product(e_4,e_2,e_4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f99,definition,
( spl0_14
<=> product(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f101,plain,
( product(e_4,e_2,e_3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f103,definition,
( spl0_15
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f105,plain,
( product(e_4,e_2,e_2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f107,definition,
( spl0_16
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f109,plain,
( product(e_4,e_2,e_1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f110,plain,
( spl0_13
| spl0_14
| spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f93,f107,f103,f99,f95]) ).
fof(f112,definition,
( spl0_17
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f114,plain,
( product(e_3,e_2,e_4)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl0_18
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f117,plain,
( ~ product(e_3,e_2,e_3)
| spl0_18 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f118,plain,
( product(e_3,e_2,e_3)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f120,definition,
( spl0_19
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f122,plain,
( product(e_3,e_2,e_2)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f124,definition,
( spl0_20
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f126,plain,
( product(e_3,e_2,e_1)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_17
| spl0_18
| spl0_19
| spl0_20 ),
inference(avatar_split_clause,[],[f92,f124,f120,f116,f112]) ).
fof(f129,definition,
( spl0_21
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f131,plain,
( product(e_1,e_2,e_4)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,definition,
( spl0_22
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f135,plain,
( product(e_1,e_2,e_3)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f137,definition,
( spl0_23
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f139,plain,
( product(e_1,e_2,e_2)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f141,definition,
( spl0_24
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f142,plain,
( ~ product(e_1,e_2,e_1)
| spl0_24 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f143,plain,
( product(e_1,e_2,e_1)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_21
| spl0_22
| spl0_23
| spl0_24 ),
inference(avatar_split_clause,[],[f90,f141,f137,f133,f129]) ).
fof(f146,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(resolution,[],[f31,f2]) ).
fof(f148,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(resolution,[],[f31,f4]) ).
fof(f150,definition,
( spl0_25
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f152,plain,
( product(e_4,e_3,e_4)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f154,definition,
( spl0_26
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f156,plain,
( product(e_4,e_3,e_3)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f158,definition,
( spl0_27
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f160,plain,
( product(e_4,e_3,e_2)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f162,definition,
( spl0_28
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f164,plain,
( product(e_4,e_3,e_1)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f165,plain,
( spl0_25
| spl0_26
| spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f148,f162,f158,f154,f150]) ).
fof(f167,definition,
( spl0_29
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f169,plain,
( product(e_2,e_3,e_4)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f171,definition,
( spl0_30
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f173,plain,
( product(e_2,e_3,e_3)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f175,definition,
( spl0_31
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f176,plain,
( ~ product(e_2,e_3,e_2)
| spl0_31 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f177,plain,
( product(e_2,e_3,e_2)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f179,definition,
( spl0_32
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f181,plain,
( product(e_2,e_3,e_1)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f182,plain,
( spl0_29
| spl0_30
| spl0_31
| spl0_32 ),
inference(avatar_split_clause,[],[f146,f179,f175,f171,f167]) ).
fof(f192,definition,
( spl0_35
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f194,plain,
( product(e_1,e_3,e_2)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f196,definition,
( spl0_36
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f198,plain,
( product(e_1,e_3,e_1)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f196]) ).
fof(f258,plain,
( ! [X0] :
( ~ product(e_1,X0,e_4)
| product(e_3,e_1,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f46,f22]) ).
fof(f271,plain,
( equalish(e_2,e_4)
| ~ spl0_13 ),
inference(resolution,[],[f97,f26]) ).
fof(f273,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f271,f10]) ).
fof(f274,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f273]) ).
fof(f278,plain,
( ! [X0] :
( ~ product(e_2,X0,e_4)
| product(e_3,e_2,X0) )
| ~ spl0_14 ),
inference(resolution,[],[f101,f22]) ).
fof(f289,plain,
( ! [X0] :
( ~ product(e_1,X0,e_2)
| product(e_3,e_1,X0) )
| ~ spl0_10 ),
inference(resolution,[],[f80,f22]) ).
fof(f295,plain,
( equalish(e_1,e_2)
| ~ spl0_11 ),
inference(resolution,[],[f84,f26]) ).
fof(f297,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f295,f5]) ).
fof(f298,plain,
~ spl0_11,
inference(avatar_contradiction_clause,[],[f297]) ).
fof(f303,plain,
( equalish(e_2,e_1)
| ~ spl0_12 ),
inference(resolution,[],[f88,f27]) ).
fof(f304,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f303,f8]) ).
fof(f305,plain,
~ spl0_12,
inference(avatar_contradiction_clause,[],[f304]) ).
fof(f314,plain,
( equalish(e_4,e_2)
| ~ spl0_15 ),
inference(resolution,[],[f105,f27]) ).
fof(f315,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f314,f15]) ).
fof(f316,plain,
~ spl0_15,
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f320,plain,
( ! [X0] :
( ~ product(e_2,X0,e_4)
| product(e_1,e_2,X0) )
| ~ spl0_16 ),
inference(resolution,[],[f109,f22]) ).
fof(f321,plain,
( product(e_3,e_1,e_2)
| ~ spl0_2
| ~ spl0_21 ),
inference(resolution,[],[f131,f258]) ).
fof(f326,plain,
( spl0_7
| ~ spl0_2
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f321,f129,f44,f65]) ).
fof(f331,plain,
( equalish(e_4,e_1)
| ~ spl0_4 ),
inference(resolution,[],[f54,f27]) ).
fof(f332,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f331,f14]) ).
fof(f333,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f332]) ).
fof(f334,plain,
( product(e_1,e_2,e_1)
| ~ spl0_9
| ~ spl0_16 ),
inference(resolution,[],[f320,f76]) ).
fof(f335,plain,
( spl0_24
| ~ spl0_9
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f334,f107,f74,f141]) ).
fof(f340,plain,
( equalish(e_1,e_4)
| ~ spl0_1 ),
inference(resolution,[],[f42,f26]) ).
fof(f342,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f340,f7]) ).
fof(f343,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f342]) ).
fof(f347,plain,
( ! [X0] :
( ~ product(e_1,X0,e_4)
| product(e_2,e_1,X0) )
| ~ spl0_3 ),
inference(resolution,[],[f50,f22]) ).
fof(f348,plain,
( product(e_2,e_1,e_2)
| ~ spl0_3
| ~ spl0_21 ),
inference(resolution,[],[f347,f131]) ).
fof(f349,plain,
( $false
| ~ spl0_3
| spl0_11
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f348,f83]) ).
fof(f350,plain,
( ~ spl0_3
| spl0_11
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f355,plain,
( equalish(e_2,e_1)
| ~ spl0_24 ),
inference(resolution,[],[f143,f26]) ).
fof(f357,plain,
( $false
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f355,f8]) ).
fof(f358,plain,
~ spl0_24,
inference(avatar_contradiction_clause,[],[f357]) ).
fof(f366,plain,
( ! [X0] :
( ~ product(e_2,X0,e_3)
| product(e_1,e_2,X0) )
| ~ spl0_20 ),
inference(resolution,[],[f126,f22]) ).
fof(f372,plain,
( ! [X0] :
( ~ product(e_2,X0,e_1)
| product(e_3,e_2,X0) )
| ~ spl0_22 ),
inference(resolution,[],[f135,f22]) ).
fof(f377,plain,
( equalish(e_3,e_4)
| ~ spl0_25 ),
inference(resolution,[],[f152,f26]) ).
fof(f379,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f377,f13]) ).
fof(f380,plain,
~ spl0_25,
inference(avatar_contradiction_clause,[],[f379]) ).
fof(f384,plain,
( ! [X0] :
( ~ product(e_3,X0,e_4)
| product(e_1,e_3,X0) )
| ~ spl0_28 ),
inference(resolution,[],[f164,f22]) ).
fof(f385,plain,
( product(e_3,e_2,e_3)
| ~ spl0_14
| ~ spl0_29 ),
inference(resolution,[],[f169,f278]) ).
fof(f390,plain,
( spl0_18
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f385,f167,f99,f116]) ).
fof(f395,plain,
( equalish(e_2,e_3)
| ~ spl0_18 ),
inference(resolution,[],[f118,f26]) ).
fof(f397,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f395,f9]) ).
fof(f398,plain,
~ spl0_18,
inference(avatar_contradiction_clause,[],[f397]) ).
fof(f405,plain,
( equalish(e_2,e_3)
| ~ spl0_30 ),
inference(resolution,[],[f173,f27]) ).
fof(f406,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f405,f9]) ).
fof(f407,plain,
~ spl0_30,
inference(avatar_contradiction_clause,[],[f406]) ).
fof(f409,plain,
( product(e_1,e_3,e_2)
| ~ spl0_17
| ~ spl0_28 ),
inference(resolution,[],[f384,f114]) ).
fof(f410,plain,
( spl0_35
| ~ spl0_17
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f409,f162,f112,f192]) ).
fof(f416,plain,
( equalish(e_4,e_3)
| ~ spl0_26 ),
inference(resolution,[],[f156,f27]) ).
fof(f417,plain,
( $false
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f416,f16]) ).
fof(f418,plain,
~ spl0_26,
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f422,plain,
( ! [X0] :
( ~ product(e_3,X0,e_4)
| product(e_2,e_3,X0) )
| ~ spl0_27 ),
inference(resolution,[],[f160,f22]) ).
fof(f427,plain,
( equalish(e_3,e_2)
| ~ spl0_31 ),
inference(resolution,[],[f177,f26]) ).
fof(f429,plain,
( $false
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f427,f12]) ).
fof(f430,plain,
~ spl0_31,
inference(avatar_contradiction_clause,[],[f429]) ).
fof(f431,plain,
( product(e_3,e_2,e_3)
| ~ spl0_22
| ~ spl0_32 ),
inference(resolution,[],[f181,f372]) ).
fof(f435,plain,
( ! [X0] :
( ~ product(e_3,X0,e_2)
| product(e_1,e_3,X0) )
| ~ spl0_32 ),
inference(resolution,[],[f181,f22]) ).
fof(f436,plain,
( $false
| spl0_18
| ~ spl0_22
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f431,f117]) ).
fof(f437,plain,
( spl0_18
| ~ spl0_22
| ~ spl0_32 ),
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f439,plain,
( product(e_2,e_3,e_2)
| ~ spl0_17
| ~ spl0_27 ),
inference(resolution,[],[f422,f114]) ).
fof(f440,plain,
( $false
| ~ spl0_17
| ~ spl0_27
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f439,f176]) ).
fof(f441,plain,
( ~ spl0_17
| ~ spl0_27
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f447,plain,
( equalish(e_1,e_3)
| ~ spl0_6 ),
inference(resolution,[],[f63,f26]) ).
fof(f449,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f447,f6]) ).
fof(f450,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f449]) ).
fof(f468,plain,
( equalish(e_1,e_2)
| ~ spl0_23 ),
inference(resolution,[],[f139,f27]) ).
fof(f469,plain,
( $false
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f468,f5]) ).
fof(f470,plain,
~ spl0_23,
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f471,plain,
( product(e_1,e_2,e_1)
| ~ spl0_10
| ~ spl0_20 ),
inference(resolution,[],[f80,f366]) ).
fof(f477,plain,
( $false
| ~ spl0_10
| ~ spl0_20
| spl0_24 ),
inference(forward_subsumption_resolution,[],[f471,f142]) ).
fof(f478,plain,
( ~ spl0_10
| ~ spl0_20
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f477]) ).
fof(f502,plain,
( product(e_3,e_1,e_3)
| ~ spl0_10
| ~ spl0_35 ),
inference(resolution,[],[f194,f289]) ).
fof(f507,plain,
( $false
| spl0_6
| ~ spl0_10
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f502,f62]) ).
fof(f508,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f507]) ).
fof(f514,plain,
( equalish(e_3,e_2)
| ~ spl0_19 ),
inference(resolution,[],[f122,f27]) ).
fof(f515,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f514,f12]) ).
fof(f516,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f557,plain,
( equalish(e_3,e_1)
| ~ spl0_36 ),
inference(resolution,[],[f198,f26]) ).
fof(f559,plain,
( $false
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f557,f11]) ).
fof(f560,plain,
~ spl0_36,
inference(avatar_contradiction_clause,[],[f559]) ).
fof(f568,plain,
( product(e_1,e_3,e_1)
| ~ spl0_7
| ~ spl0_32 ),
inference(resolution,[],[f435,f67]) ).
fof(f569,plain,
( spl0_36
| ~ spl0_7
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f568,f179,f65,f196]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f55]) ).
cnf(s3,plain,
( spl0_9
| spl0_10
| spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f89]) ).
cnf(s4,plain,
( spl0_13
| spl0_14
| spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
( spl0_17
| spl0_18
| spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f127]) ).
cnf(s6,plain,
( spl0_21
| spl0_22
| spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f144]) ).
cnf(s7,plain,
( spl0_25
| spl0_26
| spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f165]) ).
cnf(s8,plain,
( spl0_29
| spl0_30
| spl0_31
| spl0_32 ),
inference(sat_conversion,[],[f182]) ).
cnf(s13,plain,
~ spl0_13,
inference(sat_conversion,[],[f274]) ).
cnf(s16,plain,
~ spl0_11,
inference(sat_conversion,[],[f298]) ).
cnf(s17,plain,
~ spl0_12,
inference(sat_conversion,[],[f305]) ).
cnf(s18,plain,
~ spl0_15,
inference(sat_conversion,[],[f316]) ).
cnf(s19,plain,
( ~ spl0_2
| spl0_7
| ~ spl0_21 ),
inference(sat_conversion,[],[f326]) ).
cnf(s20,plain,
~ spl0_4,
inference(sat_conversion,[],[f333]) ).
cnf(s21,plain,
( ~ spl0_9
| ~ spl0_16
| spl0_24 ),
inference(sat_conversion,[],[f335]) ).
cnf(s22,plain,
~ spl0_1,
inference(sat_conversion,[],[f343]) ).
cnf(s23,plain,
( ~ spl0_3
| spl0_11
| ~ spl0_21 ),
inference(sat_conversion,[],[f350]) ).
cnf(s24,plain,
~ spl0_24,
inference(sat_conversion,[],[f358]) ).
cnf(s26,plain,
~ spl0_25,
inference(sat_conversion,[],[f380]) ).
cnf(s27,plain,
( ~ spl0_14
| spl0_18
| ~ spl0_29 ),
inference(sat_conversion,[],[f390]) ).
cnf(s28,plain,
~ spl0_18,
inference(sat_conversion,[],[f398]) ).
cnf(s29,plain,
~ spl0_30,
inference(sat_conversion,[],[f407]) ).
cnf(s30,plain,
( ~ spl0_17
| ~ spl0_28
| spl0_35 ),
inference(sat_conversion,[],[f410]) ).
cnf(s32,plain,
~ spl0_26,
inference(sat_conversion,[],[f418]) ).
cnf(s33,plain,
~ spl0_31,
inference(sat_conversion,[],[f430]) ).
cnf(s34,plain,
( spl0_18
| ~ spl0_22
| ~ spl0_32 ),
inference(sat_conversion,[],[f437]) ).
cnf(s35,plain,
( ~ spl0_17
| ~ spl0_27
| spl0_31 ),
inference(sat_conversion,[],[f441]) ).
cnf(s38,plain,
~ spl0_6,
inference(sat_conversion,[],[f450]) ).
cnf(s42,plain,
~ spl0_23,
inference(sat_conversion,[],[f470]) ).
cnf(s45,plain,
( ~ spl0_10
| ~ spl0_20
| spl0_24 ),
inference(sat_conversion,[],[f478]) ).
cnf(s46,plain,
( spl0_6
| ~ spl0_10
| ~ spl0_35 ),
inference(sat_conversion,[],[f508]) ).
cnf(s47,plain,
~ spl0_19,
inference(sat_conversion,[],[f516]) ).
cnf(s53,plain,
~ spl0_36,
inference(sat_conversion,[],[f560]) ).
cnf(s55,plain,
( ~ spl0_7
| ~ spl0_32
| spl0_36 ),
inference(sat_conversion,[],[f569]) ).
cnf(s57,plain,
( ~ spl0_14
| ~ spl0_29 ),
inference(rat,[],[s27,s28]) ).
cnf(s58,plain,
( ~ spl0_9
| ~ spl0_16 ),
inference(rat,[],[s21,s24]) ).
cnf(s60,plain,
( spl0_29
| spl0_32 ),
inference(rat,[],[s8,s33,s29]) ).
cnf(s61,plain,
( spl0_27
| spl0_28 ),
inference(rat,[],[s7,s32,s26]) ).
cnf(s62,plain,
( spl0_21
| spl0_22 ),
inference(rat,[],[s6,s24,s42]) ).
cnf(s63,plain,
( spl0_17
| spl0_20 ),
inference(rat,[],[s5,s47,s28]) ).
cnf(s64,plain,
( spl0_14
| spl0_16 ),
inference(rat,[],[s4,s18,s13]) ).
cnf(s65,plain,
( spl0_9
| spl0_10 ),
inference(rat,[],[s3,s17,s16]) ).
cnf(s67,plain,
( spl0_2
| spl0_3 ),
inference(rat,[],[s1,s20,s22]) ).
cnf(s68,plain,
~ spl0_10,
inference(rat,[],[s61,s30,s35,s63,s45,s46,s33,s24,s38]) ).
cnf(s69,plain,
spl0_9,
inference(rat,[],[s65,s68]) ).
cnf(s70,plain,
~ spl0_16,
inference(rat,[],[s58,s69]) ).
cnf(s71,plain,
spl0_14,
inference(rat,[],[s64,s70]) ).
cnf(s72,plain,
~ spl0_29,
inference(rat,[],[s57,s71]) ).
cnf(s74,plain,
spl0_32,
inference(rat,[],[s60,s72]) ).
cnf(s75,plain,
~ spl0_7,
inference(rat,[],[s55,s53,s74]) ).
cnf(s76,plain,
~ spl0_22,
inference(rat,[],[s34,s28,s74]) ).
cnf(s78,plain,
spl0_21,
inference(rat,[],[s62,s76]) ).
cnf(s80,plain,
~ spl0_3,
inference(rat,[],[s23,s16,s78]) ).
cnf(s81,plain,
~ spl0_2,
inference(rat,[],[s19,s75,s78]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s67,s80,s81]) ).
fof(f570,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP127-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:27:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.38 Running first-order model finding
% 0.14/0.38 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
% 0.14/0.42 % (2071133)Will run a generic schedule for satisfiability detection.
% 0.14/0.42 % (2071139)% WARNING: option uhcvi not known.
% 0.14/0.42 % (2071139)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1373545913:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.42 % (2071139) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2071133-2071139"...
% 0.14/0.42 % (2071138)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1433945455_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.42 % (2071140)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1365836952:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.42 % (2071139)...printing done.
% 0.14/0.42 % (2071141)dis+10_1_sil=32000:sp=arity:random_seed=748902133:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.42 % (2071142)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2036747609:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.42 % (2071139)Refutation found. Thanks to Tanya!
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.42 % (2071139)------------------------------
% 0.14/0.42 % (2071139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.42 % (2071139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.42 % (2071139)CaDiCaL version: 2.1.3
% 0.14/0.42 % (2071139)Termination reason: Refutation
% 0.14/0.42 % (2071139)Time elapsed: 0.006 s
% 0.14/0.42 % (2071139)Peak memory usage: 12 MB
% 0.14/0.42 % (2071139)Instructions burned: 16 (million)
% 0.14/0.42 % (2071133)Success in time 0.031 s
% 0.14/0.42 % Vampire exiting
%------------------------------------------------------------------------------