%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:12:41 AM UTC 2026
% Result : Unsatisfiable 1.51s 1.03s
% Output : Refutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 170 ( 50 unt; 20 def)
% Number of atoms : 357 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 357 ( 170 ~; 167 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 26 ( 25 usr; 21 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
fof(f9,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_3) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
fof(f11,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f12,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f13,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f14,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f15,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f16,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f17,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f18,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f19,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f20,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f21,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f22,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f23,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f26,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f27,axiom,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| 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(f29,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f30,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f31,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f33,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X3,X4,X2)
| ~ product(X5,X0,X1)
| ~ product(X5,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
fof(f39,definition,
( spl0_1
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f40,plain,
( product(e_1,e_2,e_2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_3)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f16,f33]) ).
fof(f56,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_1,X1)
| ~ product(X2,X3,e_1)
| ~ product(X2,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(resolution,[],[f17,f33]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_2,X1)
| ~ product(X2,X3,e_2)
| ~ product(X2,X0,e_3)
| ~ product(X0,e_3,X1) ),
inference(resolution,[],[f19,f33]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,e_2,X1)
| ~ product(X2,X3,e_2)
| ~ product(X2,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(resolution,[],[f20,f33]) ).
fof(f84,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(factoring,[],[f54]) ).
fof(f87,definition,
( spl0_9
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f88,plain,
( product(e_1,e_3,e_3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f122,plain,
! [X0] :
( ~ product(e_1,e_1,e_1)
| ~ product(e_1,X0,e_4)
| ~ product(X0,e_4,e_1) ),
inference(factoring,[],[f56]) ).
fof(f143,plain,
! [X0] :
( ~ product(e_1,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(forward_subsumption_resolution,[],[f84,f31]) ).
fof(f144,plain,
! [X0] :
( ~ product(e_1,X0,e_4)
| ~ product(X0,e_4,e_1) ),
inference(forward_subsumption_resolution,[],[f122,f31]) ).
fof(f147,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f29,f31]) ).
fof(f149,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f30,f31]) ).
fof(f151,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| product(e_1,X0,e_3)
| product(e_1,X0,e_4) ),
inference(resolution,[],[f27,f11]) ).
fof(f166,plain,
! [X0] :
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(factoring,[],[f78]) ).
fof(f169,definition,
( spl0_19
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f170,plain,
( product(e_2,e_3,e_3)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f171,plain,
( ~ product(e_2,e_3,e_3)
| spl0_19 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f176,plain,
! [X0] :
( ~ product(e_2,X0,e_3)
| ~ product(X0,e_3,e_2) ),
inference(forward_subsumption_resolution,[],[f166,f31]) ).
fof(f190,plain,
! [X0] :
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,e_2) ),
inference(factoring,[],[f80]) ).
fof(f200,plain,
! [X0] :
( ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,e_2) ),
inference(forward_subsumption_resolution,[],[f190,f31]) ).
fof(f217,definition,
( spl0_27
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f218,plain,
( product(e_3,e_4,e_4)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f238,plain,
! [X0] :
( ~ group_element(X0)
| product(e_2,X0,e_1)
| product(e_2,X0,e_2)
| product(e_2,X0,e_3)
| product(e_2,X0,e_4) ),
inference(resolution,[],[f12,f27]) ).
fof(f240,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3)
| product(e_3,X0,e_4) ),
inference(resolution,[],[f13,f27]) ).
fof(f251,plain,
! [X0] :
( ~ product(X0,e_1,e_4)
| ~ next(X0,e_3) ),
inference(resolution,[],[f9,f10]) ).
fof(f260,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,[],[f151,f12]) ).
fof(f261,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(resolution,[],[f151,f13]) ).
fof(f280,definition,
( spl0_34
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f282,plain,
( product(e_1,e_3,e_4)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f284,definition,
( spl0_35
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f288,definition,
( spl0_36
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f290,plain,
( product(e_1,e_3,e_1)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f293,definition,
( spl0_37
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_37])],[avatar_definition]) ).
fof(f295,plain,
( product(e_1,e_2,e_4)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f297,definition,
( spl0_38
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_38])],[avatar_definition]) ).
fof(f299,plain,
( product(e_1,e_2,e_3)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f301,definition,
( spl0_39
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f303,plain,
( product(e_1,e_2,e_1)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f310,plain,
( spl0_34
| spl0_9
| spl0_35
| spl0_36 ),
inference(avatar_split_clause,[],[f261,f288,f284,f87,f280]) ).
fof(f316,plain,
( spl0_37
| spl0_38
| spl0_1
| spl0_39 ),
inference(avatar_split_clause,[],[f260,f301,f39,f297,f293]) ).
fof(f324,plain,
( equalish(e_2,e_1)
| ~ spl0_1 ),
inference(resolution,[],[f40,f149]) ).
fof(f325,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f324,f18]) ).
fof(f326,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f333,plain,
( equalish(e_3,e_1)
| ~ spl0_9 ),
inference(resolution,[],[f88,f149]) ).
fof(f334,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f333,f21]) ).
fof(f335,plain,
~ spl0_9,
inference(avatar_contradiction_clause,[],[f334]) ).
fof(f343,plain,
( ~ product(e_3,e_4,e_1)
| ~ spl0_34 ),
inference(resolution,[],[f282,f144]) ).
fof(f346,plain,
( ! [X0] :
( ~ product(e_1,X0,e_4)
| equalish(e_3,X0) )
| ~ spl0_34 ),
inference(resolution,[],[f282,f29]) ).
fof(f355,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,[],[f238,f11]) ).
fof(f357,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,[],[f238,f13]) ).
fof(f360,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f357,f171]) ).
fof(f362,definition,
( spl0_42
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f364,plain,
( product(e_2,e_1,e_4)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f366,definition,
( spl0_43
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f368,plain,
( product(e_2,e_1,e_3)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f370,definition,
( spl0_44
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f372,plain,
( product(e_2,e_1,e_2)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f374,definition,
( spl0_45
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f376,plain,
( product(e_2,e_1,e_1)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f377,plain,
( spl0_42
| spl0_43
| spl0_44
| spl0_45 ),
inference(avatar_split_clause,[],[f355,f374,f370,f366,f362]) ).
fof(f392,definition,
( spl0_49
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f394,plain,
( product(e_2,e_3,e_4)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f396,definition,
( spl0_50
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f398,plain,
( product(e_2,e_3,e_2)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f400,definition,
( spl0_51
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f402,plain,
( product(e_2,e_3,e_1)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f403,plain,
( spl0_49
| spl0_50
| spl0_51
| spl0_19 ),
inference(avatar_split_clause,[],[f360,f169,f400,f396,f392]) ).
fof(f423,plain,
( equalish(e_3,e_2)
| ~ spl0_19 ),
inference(resolution,[],[f170,f149]) ).
fof(f424,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f423,f22]) ).
fof(f425,plain,
~ spl0_19,
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f446,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_4) ),
inference(resolution,[],[f240,f14]) ).
fof(f483,definition,
( spl0_62
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[spl0_62])],[avatar_definition]) ).
fof(f485,plain,
( product(e_3,e_4,e_3)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f487,definition,
( spl0_63
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[spl0_63])],[avatar_definition]) ).
fof(f491,definition,
( spl0_64
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f500,plain,
( spl0_27
| spl0_62
| spl0_63
| spl0_64 ),
inference(avatar_split_clause,[],[f446,f491,f487,f483,f217]) ).
fof(f508,plain,
( equalish(e_4,e_3)
| ~ spl0_27 ),
inference(resolution,[],[f218,f149]) ).
fof(f509,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f508,f26]) ).
fof(f510,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f509]) ).
fof(f512,plain,
( ~ product(e_3,e_4,e_2)
| ~ spl0_49 ),
inference(resolution,[],[f394,f200]) ).
fof(f518,plain,
( ~ spl0_63
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f512,f392,f487]) ).
fof(f582,plain,
( equalish(e_3,e_4)
| ~ spl0_62 ),
inference(resolution,[],[f485,f147]) ).
fof(f583,plain,
( $false
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f582,f23]) ).
fof(f584,plain,
~ spl0_62,
inference(avatar_contradiction_clause,[],[f583]) ).
fof(f591,plain,
( equalish(e_2,e_3)
| ~ spl0_50 ),
inference(resolution,[],[f398,f147]) ).
fof(f592,plain,
( $false
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f591,f19]) ).
fof(f593,plain,
~ spl0_50,
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f610,plain,
( ~ next(e_2,e_3)
| ~ spl0_42 ),
inference(resolution,[],[f364,f251]) ).
fof(f619,plain,
( $false
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f610,f2]) ).
fof(f620,plain,
~ spl0_42,
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f624,plain,
( ~ spl0_64
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f343,f280,f491]) ).
fof(f629,plain,
( ~ product(e_1,e_3,e_2)
| ~ spl0_43 ),
inference(resolution,[],[f368,f176]) ).
fof(f640,plain,
( ~ spl0_35
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f629,f366,f284]) ).
fof(f667,plain,
( ~ product(e_2,e_3,e_1)
| ~ spl0_38 ),
inference(resolution,[],[f299,f143]) ).
fof(f674,plain,
( $false
| ~ spl0_38
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[],[f667,f402]) ).
fof(f675,plain,
( ~ spl0_38
| ~ spl0_51 ),
inference(avatar_contradiction_clause,[],[f674]) ).
fof(f682,plain,
( equalish(e_1,e_2)
| ~ spl0_39 ),
inference(resolution,[],[f303,f147]) ).
fof(f683,plain,
( $false
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f682,f15]) ).
fof(f684,plain,
~ spl0_39,
inference(avatar_contradiction_clause,[],[f683]) ).
fof(f738,plain,
( equalish(e_3,e_2)
| ~ spl0_34
| ~ spl0_37 ),
inference(resolution,[],[f346,f295]) ).
fof(f740,plain,
( $false
| ~ spl0_34
| ~ spl0_37 ),
inference(forward_subsumption_resolution,[],[f738,f22]) ).
fof(f741,plain,
( ~ spl0_34
| ~ spl0_37 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f747,plain,
( equalish(e_1,e_3)
| ~ spl0_36 ),
inference(resolution,[],[f290,f147]) ).
fof(f748,plain,
( $false
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f747,f16]) ).
fof(f749,plain,
~ spl0_36,
inference(avatar_contradiction_clause,[],[f748]) ).
fof(f769,plain,
( equalish(e_2,e_1)
| ~ spl0_44 ),
inference(resolution,[],[f372,f147]) ).
fof(f770,plain,
( $false
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f769,f18]) ).
fof(f771,plain,
~ spl0_44,
inference(avatar_contradiction_clause,[],[f770]) ).
fof(f783,plain,
( equalish(e_1,e_2)
| ~ spl0_45 ),
inference(resolution,[],[f376,f149]) ).
fof(f784,plain,
( $false
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f783,f15]) ).
fof(f785,plain,
~ spl0_45,
inference(avatar_contradiction_clause,[],[f784]) ).
cnf(s23,plain,
( spl0_9
| spl0_34
| spl0_35
| spl0_36 ),
inference(sat_conversion,[],[f310]) ).
cnf(s25,plain,
( spl0_1
| spl0_37
| spl0_38
| spl0_39 ),
inference(sat_conversion,[],[f316]) ).
cnf(s26,plain,
~ spl0_1,
inference(sat_conversion,[],[f326]) ).
cnf(s27,plain,
~ spl0_9,
inference(sat_conversion,[],[f335]) ).
cnf(s28,plain,
( spl0_42
| spl0_43
| spl0_44
| spl0_45 ),
inference(sat_conversion,[],[f377]) ).
cnf(s30,plain,
( spl0_19
| spl0_49
| spl0_50
| spl0_51 ),
inference(sat_conversion,[],[f403]) ).
cnf(s35,plain,
~ spl0_19,
inference(sat_conversion,[],[f425]) ).
cnf(s41,plain,
( spl0_27
| spl0_62
| spl0_63
| spl0_64 ),
inference(sat_conversion,[],[f500]) ).
cnf(s42,plain,
~ spl0_27,
inference(sat_conversion,[],[f510]) ).
cnf(s43,plain,
( ~ spl0_49
| ~ spl0_63 ),
inference(sat_conversion,[],[f518]) ).
cnf(s48,plain,
~ spl0_62,
inference(sat_conversion,[],[f584]) ).
cnf(s49,plain,
~ spl0_50,
inference(sat_conversion,[],[f593]) ).
cnf(s50,plain,
~ spl0_42,
inference(sat_conversion,[],[f620]) ).
cnf(s54,plain,
( ~ spl0_34
| ~ spl0_64 ),
inference(sat_conversion,[],[f624]) ).
cnf(s57,plain,
( ~ spl0_35
| ~ spl0_43 ),
inference(sat_conversion,[],[f640]) ).
cnf(s64,plain,
( ~ spl0_38
| ~ spl0_51 ),
inference(sat_conversion,[],[f675]) ).
cnf(s65,plain,
~ spl0_39,
inference(sat_conversion,[],[f684]) ).
cnf(s76,plain,
( ~ spl0_34
| ~ spl0_37 ),
inference(sat_conversion,[],[f741]) ).
cnf(s77,plain,
~ spl0_36,
inference(sat_conversion,[],[f749]) ).
cnf(s79,plain,
~ spl0_44,
inference(sat_conversion,[],[f771]) ).
cnf(s80,plain,
~ spl0_45,
inference(sat_conversion,[],[f785]) ).
cnf(s83,plain,
( spl0_63
| spl0_64 ),
inference(rat,[],[s41,s48,s42]) ).
cnf(s88,plain,
( spl0_49
| spl0_51 ),
inference(rat,[],[s30,s49,s35]) ).
cnf(s90,plain,
spl0_43,
inference(rat,[],[s28,s80,s79,s50]) ).
cnf(s91,plain,
~ spl0_35,
inference(rat,[],[s57,s90]) ).
cnf(s92,plain,
( spl0_37
| spl0_38 ),
inference(rat,[],[s25,s65,s26]) ).
cnf(s93,plain,
spl0_34,
inference(rat,[],[s23,s77,s91,s27]) ).
cnf(s94,plain,
~ spl0_37,
inference(rat,[],[s76,s93]) ).
cnf(s95,plain,
~ spl0_64,
inference(rat,[],[s54,s93]) ).
cnf(s96,plain,
spl0_38,
inference(rat,[],[s92,s94]) ).
cnf(s97,plain,
spl0_63,
inference(rat,[],[s83,s95]) ).
cnf(s98,plain,
~ spl0_51,
inference(rat,[],[s64,s96]) ).
cnf(s99,plain,
~ spl0_49,
inference(rat,[],[s43,s97]) ).
cnf(s100,plain,
$false,
inference(rat,[],[s88,s98,s99]) ).
fof(f788,plain,
$false,
inference(avatar_sat_refutation,[],[s100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 09:19:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.51/1.03 % (2725178)Input is clausal, will run a generic CNF schedule.
% 1.51/1.03 % (2725188)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=225440485:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.51/1.03 % (2725186)lrs+10_1_sil=8000:sp=occurrence:random_seed=3945032263:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.51/1.03 % (2725184)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2511544183:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.51/1.03 % (2725187)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1254977375:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.51/1.03 % (2725189)dis-21_1_sil=8000:lcm=predicate:random_seed=668971879:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.51/1.03 % (2725183)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2359904210:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.51/1.03 % (2725185)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2476902368:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.51/1.03 % (2725187)Refutation not found, incomplete strategy
% 1.51/1.03 % (2725187)------------------------------
% 1.51/1.03 % (2725187)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.51/1.03 % (2725187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/1.03 % (2725187)CaDiCaL version: 2.1.3
% 1.51/1.03 % (2725187)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.03 % (2725187)Time elapsed: 0.002 s
% 1.51/1.03 % (2725187)Peak memory usage: 87 MB
% 1.51/1.03 % (2725187)Instructions burned: 1 (million)
% 1.51/1.03 % (2725188)First to succeed.
% 1.51/1.03 % (2725188)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2725178"
% 1.51/1.03 % (2725186)Instruction limit reached!
% 1.51/1.03 % (2725186)------------------------------
% 1.51/1.03 % (2725186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.51/1.03 % (2725186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/1.03 % (2725186)CaDiCaL version: 2.1.3
% 1.51/1.03 % (2725186)Termination reason: Instruction limit
% 1.51/1.03 % (2725186)Termination phase: Saturation
% 1.51/1.03 % (2725186)Time elapsed: 0.060 s
% 1.51/1.03 % (2725186)Peak memory usage: 88 MB
% 1.51/1.03 % (2725186)Instructions burned: 107 (million)
% 1.51/1.03 % (2725189)Instruction limit reached!
% 1.51/1.03 % (2725189)------------------------------
% 1.51/1.03 % (2725189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.51/1.03 % (2725189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/1.03 % (2725189)CaDiCaL version: 2.1.3
% 1.51/1.03 % (2725189)Termination reason: Instruction limit
% 1.51/1.03 % (2725189)Termination phase: Saturation
% 1.51/1.03 % (2725189)Time elapsed: 0.075 s
% 1.51/1.03 % (2725189)Peak memory usage: 89 MB
% 1.51/1.03 % (2725189)Instructions burned: 118 (million)
% 1.51/1.03 % (2725197)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3790871384:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 1.51/1.03 % (2725198)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1968502092:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 1.51/1.03 % (2725198)Refutation not found, incomplete strategy
% 1.51/1.03 % (2725198)------------------------------
% 1.51/1.03 % (2725198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.51/1.03 % (2725198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/1.03 % (2725198)CaDiCaL version: 2.1.3
% 1.51/1.03 % (2725198)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.03 % (2725198)Time elapsed: 0.002 s
% 1.51/1.03 % (2725198)Peak memory usage: 88 MB
% 1.51/1.03 % (2725198)Instructions burned: 2 (million)
% 1.51/1.03 % (2725187)------------------------------
% 1.51/1.03 % (2725187)------------------------------
% 1.51/1.03 % (2725188)Refutation found. Thanks to Tanya!
% 1.51/1.03 % SZS status Unsatisfiable for theBenchmark
% 1.51/1.03 % SZS output start Proof for theBenchmark
% See solution above
% 3.27/1.22 % (2725188)------------------------------
% 3.27/1.22 % (2725188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.27/1.22 % (2725188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.27/1.22 % (2725188)CaDiCaL version: 2.1.3
% 3.27/1.22 % (2725188)Termination reason: Refutation
% 3.27/1.22 % (2725188)Time elapsed: 0.014 s
% 3.27/1.22 % (2725188)Peak memory usage: 89 MB
% 3.27/1.22 % (2725188)Instructions burned: 19 (million)
% 3.27/1.22 % (2725188)------------------------------
% 3.27/1.22 % (2725188)------------------------------
% 3.27/1.22 % (2725178)Success in time 0.415 s
% 3.27/1.22 % Vampire exiting
%------------------------------------------------------------------------------