%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT039-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:02:10 PM UTC 2026
% Result : Unsatisfiable 0.71s 1.01s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 34
% Syntax : Number of formulae : 155 ( 26 unt; 16 def)
% Number of atoms : 509 ( 27 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 666 ( 312 ~; 338 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 17 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| environment(sk1(X0))
| selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy_20) ).
fof(f2,axiom,
! [X0] :
( ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| in_environment(X0,sk1(X0))
| selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy_21) ).
fof(f3,axiom,
! [X0] :
( ~ observational_period(X0)
| ~ propagation_strategy(first_movers)
| ~ propagation_strategy(efficient_producers)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0)))
| selection_favors(efficient_producers,first_movers,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp3_favoured_trategy_22) ).
fof(f4,axiom,
! [X0,X1] :
( in_environment(X1,sk2(X1,X0))
| ~ slow_change(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| ~ observational_period(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point_23) ).
fof(f5,axiom,
! [X0,X1] :
( ~ slow_change(X0)
| ~ observational_period(X0)
| ~ environment(X1)
| ~ in_environment(X0,X1)
| greater(sk2(X1,X0),critical_point(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp4_critical_point_24) ).
fof(f6,axiom,
propagation_strategy(first_movers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets1_25) ).
fof(f7,axiom,
propagation_strategy(efficient_producers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_organizational_sets2_26) ).
fof(f8,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater_or_equal(end_time(X0),X1)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_in_environment_27) ).
fof(f9,axiom,
! [X0,X1] :
( greater_or_equal(end_time(X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_end_point_28) ).
fof(f10,axiom,
! [X0] :
( greater_or_equal(critical_point(X0),start_time(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_of_critical_point_29) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ greater(X0,X1)
| ~ greater(X1,X2)
| greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).
fof(f12,axiom,
! [X0,X1] :
( greater(X0,X1)
| ~ greater_or_equal(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).
fof(f13,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
fof(f14,axiom,
! [X0,X1] :
( X0 != X1
| greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_33) ).
fof(f16,axiom,
! [X0,X1] :
( ~ greater(X1,critical_point(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| selection_favors(efficient_producers,first_movers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l8_35) ).
fof(f17,negated_conjecture,
observational_period(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8_36) ).
fof(f18,negated_conjecture,
slow_change(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8_37) ).
fof(f19,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t8_38) ).
fof(f20,plain,
! [X1] : greater_or_equal(X1,X1),
inference(equality_resolution,[],[f14]) ).
fof(f22,definition,
( spl0_1
<=> propagation_strategy(efficient_producers) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f26,definition,
( spl0_2
<=> propagation_strategy(first_movers) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f30,definition,
( spl0_3
<=> ! [X0] :
( ~ observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0))) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f31,plain,
( ! [X0] :
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(X0)))
| selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f32,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f3,f30,f26,f22]) ).
fof(f34,definition,
( spl0_4
<=> ! [X0] :
( ~ observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| in_environment(X0,sk1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f35,plain,
( ! [X0] :
( in_environment(X0,sk1(X0))
| selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f36,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f2,f34,f26,f22]) ).
fof(f38,definition,
( spl0_5
<=> ! [X0] :
( ~ observational_period(X0)
| selection_favors(efficient_producers,first_movers,X0)
| environment(sk1(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f39,plain,
( ! [X0] :
( environment(sk1(X0))
| selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f40,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f1,f38,f26,f22]) ).
fof(f41,plain,
spl0_2,
inference(avatar_split_clause,[],[f6,f26]) ).
fof(f42,plain,
spl0_1,
inference(avatar_split_clause,[],[f7,f22]) ).
fof(f44,plain,
! [X0] :
( ~ observational_period(sk3)
| ~ environment(X0)
| ~ in_environment(sk3,X0)
| greater(sk2(X0,sk3),critical_point(X0)) ),
inference(resolution,[],[f5,f18]) ).
fof(f45,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(sk3,X0)
| greater(sk2(X0,sk3),critical_point(X0)) ),
inference(forward_subsumption_resolution,[],[f44,f17]) ).
fof(f46,plain,
( ! [X0] :
( ~ in_environment(sk3,sk1(X0))
| greater(sk2(sk1(X0),sk3),critical_point(sk1(X0)))
| selection_favors(efficient_producers,first_movers,X0)
| ~ observational_period(X0) )
| ~ spl0_5 ),
inference(resolution,[],[f45,f39]) ).
fof(f48,plain,
! [X2,X0,X1] :
( greater(X0,X2)
| X0 = X1
| ~ greater(X1,X2)
| ~ greater_or_equal(X0,X1) ),
inference(resolution,[],[f12,f11]) ).
fof(f49,plain,
( greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| selection_favors(efficient_producers,first_movers,sk3)
| ~ observational_period(sk3)
| selection_favors(efficient_producers,first_movers,sk3)
| ~ observational_period(sk3)
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f46,f35]) ).
fof(f50,plain,
( greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| selection_favors(efficient_producers,first_movers,sk3)
| ~ observational_period(sk3)
| ~ spl0_4
| ~ spl0_5 ),
inference(duplicate_literal_removal,[],[f49]) ).
fof(f51,plain,
( greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ observational_period(sk3)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f50,f19]) ).
fof(f52,plain,
( greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f51,f17]) ).
fof(f53,plain,
( ! [X0,X1] :
( ~ observational_period(X1)
| ~ greater_or_equal(end_time(sk1(X1)),X0)
| in_environment(sk1(X1),X0)
| selection_favors(efficient_producers,first_movers,X1)
| ~ greater_or_equal(X0,start_time(sk1(X1))) )
| ~ spl0_5 ),
inference(resolution,[],[f8,f39]) ).
fof(f54,plain,
( ~ in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| ~ environment(sk1(sk3))
| selection_favors(efficient_producers,first_movers,sk2(sk1(sk3),sk3))
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f52,f16]) ).
fof(f55,plain,
( ! [X0] :
( greater(sk2(sk1(sk3),sk3),X0)
| ~ greater(critical_point(sk1(sk3)),X0) )
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f52,f11]) ).
fof(f57,definition,
( spl0_6
<=> selection_favors(efficient_producers,first_movers,sk2(sk1(sk3),sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f59,plain,
( selection_favors(efficient_producers,first_movers,sk2(sk1(sk3),sk3))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl0_7
<=> environment(sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f62,plain,
( environment(sk1(sk3))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f63,plain,
( ~ environment(sk1(sk3))
| spl0_7 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f65,definition,
( spl0_8
<=> in_environment(sk1(sk3),sk2(sk1(sk3),sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f66,plain,
( in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f67,plain,
( ~ in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| spl0_8 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f54,f38,f34,f65,f61,f57]) ).
fof(f69,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ observational_period(sk3)
| ~ spl0_5
| spl0_7 ),
inference(resolution,[],[f63,f39]) ).
fof(f70,plain,
( ~ observational_period(sk3)
| ~ spl0_5
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f69,f19]) ).
fof(f71,plain,
( $false
| ~ spl0_5
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f70,f17]) ).
fof(f72,plain,
( ~ spl0_5
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f73,plain,
! [X2,X0,X1] :
( selection_favors(efficient_producers,first_movers,X0)
| ~ greater(X1,critical_point(X2))
| ~ greater_or_equal(X0,X1)
| ~ in_environment(X2,X0)
| ~ environment(X2)
| X0 = X1 ),
inference(resolution,[],[f48,f16]) ).
fof(f79,plain,
( ~ slow_change(sk3)
| ~ environment(sk1(sk3))
| ~ in_environment(sk3,sk1(sk3))
| ~ observational_period(sk3)
| spl0_8 ),
inference(resolution,[],[f67,f4]) ).
fof(f80,plain,
( ~ environment(sk1(sk3))
| ~ in_environment(sk3,sk1(sk3))
| ~ observational_period(sk3)
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f79,f18]) ).
fof(f81,plain,
( ~ in_environment(sk3,sk1(sk3))
| ~ observational_period(sk3)
| ~ spl0_7
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f80,f62]) ).
fof(f82,plain,
( ~ in_environment(sk3,sk1(sk3))
| ~ spl0_7
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f81,f17]) ).
fof(f83,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| in_environment(sk1(sk3),X0)
| selection_favors(efficient_producers,first_movers,sk3)
| ~ greater_or_equal(X0,start_time(sk1(sk3))) )
| ~ spl0_5 ),
inference(resolution,[],[f53,f17]) ).
fof(f84,plain,
( ! [X0] :
( in_environment(sk1(sk3),X0)
| ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ greater_or_equal(X0,start_time(sk1(sk3))) )
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f83,f19]) ).
fof(f85,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ observational_period(sk3)
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(resolution,[],[f82,f35]) ).
fof(f86,plain,
( ~ observational_period(sk3)
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f85,f19]) ).
fof(f87,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f86,f17]) ).
fof(f88,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f87]) ).
fof(f115,plain,
( ! [X2,X0,X1] :
( ~ observational_period(X2)
| ~ greater_or_equal(end_time(sk1(X2)),X0)
| ~ in_environment(X1,end_time(sk1(X2)))
| ~ environment(X1)
| end_time(sk1(X2)) = X0
| selection_favors(efficient_producers,first_movers,X2)
| ~ greater(X0,critical_point(X1)) )
| ~ spl0_3 ),
inference(resolution,[],[f73,f31]) ).
fof(f131,definition,
( spl0_14
<=> greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f133,plain,
( ~ greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3)))
| spl0_14 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f139,definition,
( spl0_16
<=> greater_or_equal(end_time(sk1(sk3)),critical_point(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f141,plain,
( ~ greater_or_equal(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| spl0_16 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f152,plain,
( ~ greater(end_time(sk1(sk3)),start_time(sk1(sk3)))
| spl0_14 ),
inference(resolution,[],[f133,f13]) ).
fof(f167,plain,
( ! [X0,X1] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ in_environment(X1,end_time(sk1(sk3)))
| ~ environment(X1)
| end_time(sk1(sk3)) = X0
| selection_favors(efficient_producers,first_movers,sk3)
| ~ greater(X0,critical_point(X1)) )
| ~ spl0_3 ),
inference(resolution,[],[f115,f17]) ).
fof(f168,plain,
( ! [X0,X1] :
( ~ in_environment(X1,end_time(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ environment(X1)
| end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(X1)) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f167,f19]) ).
fof(f171,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ greater(X0,start_time(sk1(sk3)))
| end_time(sk1(sk3)) = X0 )
| spl0_14 ),
inference(resolution,[],[f152,f48]) ).
fof(f190,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ environment(sk1(sk3))
| end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),end_time(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3))) )
| ~ spl0_3
| ~ spl0_5 ),
inference(resolution,[],[f168,f84]) ).
fof(f228,plain,
( ! [X0] :
( ~ greater(X0,start_time(sk1(sk3)))
| end_time(sk1(sk3)) = X0
| ~ in_environment(sk1(sk3),X0)
| ~ environment(sk1(sk3)) )
| spl0_14 ),
inference(resolution,[],[f171,f9]) ).
fof(f232,plain,
( ! [X0] :
( ~ in_environment(sk1(sk3),X0)
| end_time(sk1(sk3)) = X0
| ~ greater(X0,start_time(sk1(sk3))) )
| ~ spl0_7
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f228,f62]) ).
fof(f237,plain,
( sk2(sk1(sk3),sk3) = end_time(sk1(sk3))
| ~ greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3)))
| ~ spl0_7
| ~ spl0_8
| spl0_14 ),
inference(resolution,[],[f232,f66]) ).
fof(f259,definition,
( spl0_23
<=> greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f261,plain,
( ~ greater(sk2(sk1(sk3),sk3),start_time(sk1(sk3)))
| spl0_23 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f263,definition,
( spl0_24
<=> sk2(sk1(sk3),sk3) = end_time(sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f264,plain,
( sk2(sk1(sk3),sk3) != end_time(sk1(sk3))
| spl0_24 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f265,plain,
( sk2(sk1(sk3),sk3) = end_time(sk1(sk3))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( ~ spl0_23
| spl0_24
| ~ spl0_7
| ~ spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f237,f131,f65,f61,f263,f259]) ).
fof(f271,plain,
( ~ greater(critical_point(sk1(sk3)),start_time(sk1(sk3)))
| ~ spl0_4
| ~ spl0_5
| spl0_23 ),
inference(resolution,[],[f261,f55]) ).
fof(f309,plain,
( ~ greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3)))
| critical_point(sk1(sk3)) = start_time(sk1(sk3))
| ~ spl0_4
| ~ spl0_5
| spl0_23 ),
inference(resolution,[],[f271,f12]) ).
fof(f311,definition,
( spl0_29
<=> critical_point(sk1(sk3)) = start_time(sk1(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f313,plain,
( critical_point(sk1(sk3)) = start_time(sk1(sk3))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f315,definition,
( spl0_30
<=> greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f317,plain,
( ~ greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3)))
| spl0_30 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f318,plain,
( spl0_29
| ~ spl0_30
| ~ spl0_4
| ~ spl0_5
| spl0_23 ),
inference(avatar_split_clause,[],[f309,f259,f38,f34,f315,f311]) ).
fof(f340,plain,
( ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| spl0_16 ),
inference(resolution,[],[f141,f13]) ).
fof(f375,plain,
( selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ spl0_6
| ~ spl0_24 ),
inference(superposition,[],[f59,f265]) ).
fof(f395,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),end_time(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f190,f62]) ).
fof(f399,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f395,f20]) ).
fof(f401,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),X0)
| end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(sk1(sk3))) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_29 ),
inference(forward_demodulation,[],[f399,f313]) ).
fof(f405,definition,
( spl0_36
<=> ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ greater(X0,critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_36])],[avatar_definition]) ).
fof(f406,plain,
( ! [X0] :
( ~ greater_or_equal(end_time(sk1(sk3)),X0)
| ~ greater(X0,critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = X0 )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f407,plain,
( spl0_36
| ~ spl0_16
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f401,f311,f61,f38,f30,f139,f405]) ).
fof(f521,definition,
( spl0_44
<=> selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f522,plain,
( ~ selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| spl0_44 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f523,plain,
( selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f528,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ observational_period(sk3)
| ~ spl0_3
| ~ spl0_44 ),
inference(resolution,[],[f523,f31]) ).
fof(f529,plain,
( ~ observational_period(sk3)
| ~ spl0_3
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f528,f19]) ).
fof(f530,plain,
( $false
| ~ spl0_3
| ~ spl0_44 ),
inference(forward_subsumption_resolution,[],[f529,f17]) ).
fof(f531,plain,
( ~ spl0_3
| ~ spl0_44 ),
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f565,plain,
( ! [X0] :
( end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),X0) )
| spl0_16 ),
inference(resolution,[],[f340,f48]) ).
fof(f567,plain,
( spl0_36
| spl0_16 ),
inference(avatar_split_clause,[],[f565,f139,f405]) ).
fof(f581,plain,
( ! [X0] :
( ~ greater(X0,critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = X0
| ~ in_environment(sk1(sk3),X0)
| ~ environment(sk1(sk3)) )
| ~ spl0_36 ),
inference(resolution,[],[f406,f9]) ).
fof(f590,plain,
( ! [X0] :
( ~ in_environment(sk1(sk3),X0)
| end_time(sk1(sk3)) = X0
| ~ greater(X0,critical_point(sk1(sk3))) )
| ~ spl0_7
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f581,f62]) ).
fof(f615,plain,
( sk2(sk1(sk3),sk3) = end_time(sk1(sk3))
| ~ greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ spl0_7
| ~ spl0_8
| ~ spl0_36 ),
inference(resolution,[],[f590,f66]) ).
fof(f619,plain,
( ~ greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ spl0_7
| ~ spl0_8
| spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f615,f264]) ).
fof(f620,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_24
| ~ spl0_36 ),
inference(forward_subsumption_resolution,[],[f619,f52]) ).
fof(f621,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_24
| ~ spl0_36 ),
inference(avatar_contradiction_clause,[],[f620]) ).
fof(f624,plain,
( ~ spl0_14
| spl0_36
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f399,f61,f38,f30,f405,f131]) ).
fof(f663,plain,
( ~ environment(sk1(sk3))
| spl0_30 ),
inference(resolution,[],[f317,f10]) ).
fof(f665,plain,
( $false
| ~ spl0_7
| spl0_30 ),
inference(forward_subsumption_resolution,[],[f663,f62]) ).
fof(f666,plain,
( ~ spl0_7
| spl0_30 ),
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f667,plain,
( $false
| ~ spl0_6
| ~ spl0_24
| spl0_44 ),
inference(forward_subsumption_resolution,[],[f375,f522]) ).
fof(f668,plain,
( ~ spl0_6
| ~ spl0_24
| spl0_44 ),
inference(avatar_contradiction_clause,[],[f667]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f36]) ).
cnf(s3,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
spl0_2,
inference(sat_conversion,[],[f41]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f42]) ).
cnf(s6,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_6
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f68]) ).
cnf(s7,plain,
( ~ spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
( ~ spl0_4
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f88]) ).
cnf(s15,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_14
| ~ spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f266]) ).
cnf(s18,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_23
| spl0_29
| ~ spl0_30 ),
inference(sat_conversion,[],[f318]) ).
cnf(s28,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_16
| ~ spl0_29
| spl0_36 ),
inference(sat_conversion,[],[f407]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_44 ),
inference(sat_conversion,[],[f531]) ).
cnf(s48,plain,
( spl0_16
| spl0_36 ),
inference(sat_conversion,[],[f567]) ).
cnf(s54,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| spl0_24
| ~ spl0_36 ),
inference(sat_conversion,[],[f621]) ).
cnf(s56,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| spl0_36 ),
inference(sat_conversion,[],[f624]) ).
cnf(s62,plain,
( ~ spl0_7
| spl0_30 ),
inference(sat_conversion,[],[f666]) ).
cnf(s63,plain,
( ~ spl0_6
| ~ spl0_24
| spl0_44 ),
inference(sat_conversion,[],[f668]) ).
cnf(s66,plain,
spl0_5,
inference(rat,[],[s3,s4,s5]) ).
cnf(s67,plain,
spl0_7,
inference(rat,[],[s7,s66]) ).
cnf(s68,plain,
spl0_30,
inference(rat,[],[s62,s67]) ).
cnf(s69,plain,
spl0_4,
inference(rat,[],[s2,s4,s5]) ).
cnf(s70,plain,
spl0_8,
inference(rat,[],[s8,s67,s69]) ).
cnf(s71,plain,
spl0_6,
inference(rat,[],[s6,s70,s67,s66,s69]) ).
cnf(s72,plain,
spl0_3,
inference(rat,[],[s1,s4,s5]) ).
cnf(s73,plain,
~ spl0_44,
inference(rat,[],[s42,s72]) ).
cnf(s74,plain,
~ spl0_24,
inference(rat,[],[s63,s71,s73]) ).
cnf(s75,plain,
~ spl0_36,
inference(rat,[],[s54,s70,s69,s67,s66,s74]) ).
cnf(s76,plain,
spl0_16,
inference(rat,[],[s48,s75]) ).
cnf(s77,plain,
~ spl0_14,
inference(rat,[],[s56,s72,s67,s66,s75]) ).
cnf(s78,plain,
~ spl0_29,
inference(rat,[],[s28,s75,s72,s67,s66,s76]) ).
cnf(s80,plain,
~ spl0_23,
inference(rat,[],[s15,s74,s70,s67,s77]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s18,s68,s69,s66,s78,s80]) ).
fof(f675,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT039-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 17:24:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.71/1.01 % (3290971)Input is clausal, will run a generic CNF schedule.
% 0.71/1.01 % (3291027)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4281553768:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 0.71/1.01 % (3291026)lrs+10_1_sil=8000:sp=occurrence:random_seed=933542580:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 0.71/1.01 % (3291028)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=834585255:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 0.71/1.01 % (3291023)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=133379120:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 0.71/1.01 % (3291029)dis-21_1_sil=8000:lcm=predicate:random_seed=2804179242:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 0.71/1.01 % (3291024)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2973494412:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 0.71/1.01 % (3291025)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2681330436:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 0.71/1.01 % (3291028)First to succeed.
% 0.71/1.01 % (3291028)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3290971"
% 0.71/1.01 % (3291029)Instruction limit reached!
% 0.71/1.01 % (3291029)------------------------------
% 0.71/1.01 % (3291029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.71/1.01 % (3291029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/1.01 % (3291029)CaDiCaL version: 2.1.3
% 0.71/1.01 % (3291029)Termination reason: Instruction limit
% 0.71/1.01 % (3291029)Termination phase: Saturation
% 0.71/1.01 % (3291029)Time elapsed: 0.045 s
% 0.71/1.01 % (3291029)Peak memory usage: 89 MB
% 0.71/1.01 % (3291029)Instructions burned: 119 (million)
% 0.71/1.01 % (3291026)Also succeeded, but the first one will report.
% 0.71/1.01 % (3291027)Instruction limit reached!
% 0.71/1.01 % (3291027)------------------------------
% 0.71/1.01 % (3291027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.71/1.01 % (3291027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/1.01 % (3291027)CaDiCaL version: 2.1.3
% 0.71/1.01 % (3291027)Termination reason: Instruction limit
% 0.71/1.01 % (3291027)Termination phase: Saturation
% 0.71/1.01 % (3291027)Time elapsed: 0.062 s
% 0.71/1.01 % (3291027)Peak memory usage: 88 MB
% 0.71/1.01 % (3291027)Instructions burned: 114 (million)
% 0.71/1.01 % (3291037)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=1184336317:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.71/1.01 % (3291037)Refutation not found, incomplete strategy
% 0.71/1.01 % (3291037)------------------------------
% 0.71/1.01 % (3291037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.71/1.01 % (3291037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/1.01 % (3291037)CaDiCaL version: 2.1.3
% 0.71/1.01 % (3291037)Termination reason: Refutation not found, incomplete strategy
% 0.71/1.01 % (3291037)Time elapsed: 0.001 s
% 0.71/1.01 % (3291037)Peak memory usage: 88 MB
% 0.71/1.01 % (3291037)Instructions burned: 1 (million)
% 0.71/1.01 % (3291038)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1186979798:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 0.71/1.01 % (3291038)Refutation not found, incomplete strategy
% 0.71/1.01 % (3291038)------------------------------
% 0.71/1.01 % (3291038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.71/1.01 % (3291038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/1.01 % (3291038)CaDiCaL version: 2.1.3
% 0.71/1.01 % (3291038)Termination reason: Refutation not found, incomplete strategy
% 0.71/1.01 % (3291038)Time elapsed: 0.002 s
% 0.71/1.01 % (3291038)Peak memory usage: 88 MB
% 0.71/1.01 % (3291038)Instructions burned: 2 (million)
% 0.71/1.01 % (3291028)Refutation found. Thanks to Tanya!
% 0.71/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.71/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 3.16/1.10 % (3291028)------------------------------
% 3.16/1.10 % (3291028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.10 % (3291028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.10 % (3291028)CaDiCaL version: 2.1.3
% 3.16/1.10 % (3291028)Termination reason: Refutation
% 3.16/1.10 % (3291028)Time elapsed: 0.023 s
% 3.16/1.10 % (3291028)Peak memory usage: 89 MB
% 3.16/1.10 % (3291028)Instructions burned: 31 (million)
% 3.16/1.10 % (3291028)------------------------------
% 3.16/1.10 % (3291028)------------------------------
% 3.16/1.10 % (3290971)Success in time 0.408 s
% 3.16/1.10 % Vampire exiting
%------------------------------------------------------------------------------