TSTP Solution File: MGT025-1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:51:25 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 46
% Syntax : Number of formulae : 133 ( 10 unt; 0 def)
% Number of atoms : 451 ( 31 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 570 ( 252 ~; 297 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 22 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f201,plain,
$false,
inference(avatar_sat_refutation,[],[f52,f61,f70,f80,f82,f88,f94,f105,f135,f140,f145,f146,f147,f148,f149,f151,f164,f169,f174,f181,f185,f190,f191,f195,f196,f200]) ).
fof(f200,plain,
( ~ spl3_7
| ~ spl3_8
| ~ spl3_19 ),
inference(avatar_split_clause,[],[f199,f162,f77,f73]) ).
fof(f73,plain,
( spl3_7
<=> environment(sk1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f77,plain,
( spl3_8
<=> in_environment(sk1,sk2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f162,plain,
( spl3_19
<=> ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f199,plain,
( ~ environment(sk1)
| ~ spl3_8
| ~ spl3_19 ),
inference(resolution,[],[f198,f79]) ).
fof(f79,plain,
( in_environment(sk1,sk2)
| ~ spl3_8 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f198,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl3_19 ),
inference(duplicate_literal_removal,[],[f197]) ).
fof(f197,plain,
( ! [X0] :
( ~ environment(X0)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ in_environment(X0,sk2) )
| ~ spl3_19 ),
inference(resolution,[],[f163,f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_30) ).
fof(f163,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2) )
| ~ spl3_19 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f196,plain,
( spl3_2
| ~ spl3_18
| spl3_19
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f175,f85,f162,f142,f49]) ).
fof(f49,plain,
( spl3_2
<=> greater(sF0,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f142,plain,
( spl3_18
<=> increases(cardinality_at_time(first_movers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).
fof(f85,plain,
( spl3_9
<=> greater(cardinality_at_time(first_movers,sk2),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f175,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| ~ increases(cardinality_at_time(first_movers,sk2))
| greater(sF0,zero)
| ~ in_environment(X0,sk2) )
| ~ spl3_9 ),
inference(forward_demodulation,[],[f171,f37]) ).
fof(f37,plain,
growth_rate(first_movers,sk2) = sF0,
introduced(function_definition,[]) ).
fof(f171,plain,
( ! [X0] :
( ~ increases(cardinality_at_time(first_movers,sk2))
| ~ environment(X0)
| greater(growth_rate(first_movers,sk2),zero)
| ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2) )
| ~ spl3_9 ),
inference(resolution,[],[f15,f87]) ).
fof(f87,plain,
( greater(cardinality_at_time(first_movers,sk2),zero)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| greater(growth_rate(X2,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ increases(cardinality_at_time(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_41) ).
fof(f195,plain,
( ~ spl3_7
| ~ spl3_8
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f194,f167,f77,f73]) ).
fof(f167,plain,
( spl3_20
<=> ! [X1] :
( ~ subpopulation(efficient_producers,X1,sk2)
| ~ environment(X1)
| ~ in_environment(X1,sk2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f194,plain,
( ~ environment(sk1)
| ~ spl3_8
| ~ spl3_20 ),
inference(resolution,[],[f193,f79]) ).
fof(f193,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ environment(X0) )
| ~ spl3_20 ),
inference(duplicate_literal_removal,[],[f192]) ).
fof(f192,plain,
( ! [X0] :
( ~ environment(X0)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ in_environment(X0,sk2) )
| ~ spl3_20 ),
inference(resolution,[],[f168,f5]) ).
fof(f5,axiom,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_31) ).
fof(f168,plain,
( ! [X1] :
( ~ subpopulation(efficient_producers,X1,sk2)
| ~ environment(X1)
| ~ in_environment(X1,sk2) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f191,plain,
( ~ spl3_12
| spl3_4
| spl3_19
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f186,f85,f162,f58,f115]) ).
fof(f115,plain,
( spl3_12
<=> decreases(cardinality_at_time(first_movers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f58,plain,
( spl3_4
<=> greater(zero,sF0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f186,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| ~ in_environment(X0,sk2)
| greater(zero,sF0)
| ~ environment(X0)
| ~ decreases(cardinality_at_time(first_movers,sk2)) )
| ~ spl3_9 ),
inference(forward_demodulation,[],[f182,f37]) ).
fof(f182,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,sk2)) )
| ~ spl3_9 ),
inference(resolution,[],[f16,f87]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X2,X1),zero)
| ~ decreases(cardinality_at_time(X2,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulation(X2,X0,X1)
| greater(zero,growth_rate(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_42) ).
fof(f190,plain,
( spl3_4
| ~ spl3_6
| ~ spl3_21 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f189,plain,
( $false
| spl3_4
| ~ spl3_6
| ~ spl3_21 ),
inference(resolution,[],[f180,f170]) ).
fof(f170,plain,
( ~ greater(zero,zero)
| spl3_4
| ~ spl3_6 ),
inference(superposition,[],[f60,f68]) ).
fof(f68,plain,
( zero = sF0
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl3_6
<=> zero = sF0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f60,plain,
( ~ greater(zero,sF0)
| spl3_4 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f180,plain,
( greater(zero,zero)
| ~ spl3_21 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f178,plain,
( spl3_21
<=> greater(zero,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f185,plain,
( ~ spl3_15
| spl3_20
| spl3_1
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f184,f91,f45,f167,f127]) ).
fof(f127,plain,
( spl3_15
<=> decreases(cardinality_at_time(efficient_producers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).
fof(f45,plain,
( spl3_1
<=> greater(zero,sF1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f91,plain,
( spl3_10
<=> greater(cardinality_at_time(efficient_producers,sk2),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f184,plain,
( ! [X1] :
( greater(zero,sF1)
| ~ environment(X1)
| ~ in_environment(X1,sk2)
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ subpopulation(efficient_producers,X1,sk2) )
| ~ spl3_10 ),
inference(forward_demodulation,[],[f183,f38]) ).
fof(f38,plain,
growth_rate(efficient_producers,sk2) = sF1,
introduced(function_definition,[]) ).
fof(f183,plain,
( ! [X1] :
( ~ environment(X1)
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ subpopulation(efficient_producers,X1,sk2)
| ~ decreases(cardinality_at_time(efficient_producers,sk2)) )
| ~ spl3_10 ),
inference(resolution,[],[f16,f93]) ).
fof(f93,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f181,plain,
( ~ spl3_18
| spl3_21
| spl3_19
| ~ spl3_6
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f176,f85,f67,f162,f178,f142]) ).
fof(f176,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ subpopulation(first_movers,X0,sk2)
| greater(zero,zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ environment(X0) )
| ~ spl3_6
| ~ spl3_9 ),
inference(forward_demodulation,[],[f175,f68]) ).
fof(f174,plain,
( ~ spl3_17
| spl3_3
| spl3_20
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f173,f91,f167,f54,f137]) ).
fof(f137,plain,
( spl3_17
<=> increases(cardinality_at_time(efficient_producers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).
fof(f54,plain,
( spl3_3
<=> greater(sF1,zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f173,plain,
( ! [X1] :
( ~ environment(X1)
| ~ in_environment(X1,sk2)
| ~ subpopulation(efficient_producers,X1,sk2)
| greater(sF1,zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2)) )
| ~ spl3_10 ),
inference(forward_demodulation,[],[f172,f38]) ).
fof(f172,plain,
( ! [X1] :
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ environment(X1)
| ~ in_environment(X1,sk2)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ subpopulation(efficient_producers,X1,sk2) )
| ~ spl3_10 ),
inference(resolution,[],[f15,f93]) ).
fof(f169,plain,
( ~ spl3_14
| spl3_20
| spl3_5
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f165,f91,f63,f167,f123]) ).
fof(f123,plain,
( spl3_14
<=> constant(cardinality_at_time(efficient_producers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).
fof(f63,plain,
( spl3_5
<=> zero = sF1 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f165,plain,
( ! [X1] :
( zero = sF1
| ~ subpopulation(efficient_producers,X1,sk2)
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) )
| ~ spl3_10 ),
inference(forward_demodulation,[],[f159,f38]) ).
fof(f159,plain,
( ! [X1] :
( ~ in_environment(X1,sk2)
| zero = growth_rate(efficient_producers,sk2)
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ subpopulation(efficient_producers,X1,sk2)
| ~ environment(X1) )
| ~ spl3_10 ),
inference(resolution,[],[f14,f93]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X2,X1),zero)
| ~ in_environment(X0,X1)
| ~ constant(cardinality_at_time(X2,X1))
| ~ environment(X0)
| ~ subpopulation(X2,X0,X1)
| zero = growth_rate(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_40) ).
fof(f164,plain,
( ~ spl3_16
| spl3_6
| spl3_19
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f160,f85,f162,f67,f132]) ).
fof(f132,plain,
( spl3_16
<=> constant(cardinality_at_time(first_movers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).
fof(f160,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sk2)
| zero = sF0
| ~ in_environment(X0,sk2)
| ~ environment(X0)
| ~ constant(cardinality_at_time(first_movers,sk2)) )
| ~ spl3_9 ),
inference(forward_demodulation,[],[f158,f37]) ).
fof(f158,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ subpopulation(first_movers,X0,sk2)
| ~ environment(X0)
| zero = growth_rate(first_movers,sk2) )
| ~ spl3_9 ),
inference(resolution,[],[f14,f87]) ).
fof(f151,plain,
spl3_13,
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f150,plain,
( $false
| spl3_13 ),
inference(resolution,[],[f121,f41]) ).
fof(f41,plain,
constant(sF2),
inference(definition_folding,[],[f23,f40]) ).
fof(f40,plain,
number_of_organizations(sk1,sk2) = sF2,
introduced(function_definition,[]) ).
fof(f23,axiom,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_49) ).
fof(f121,plain,
( ~ constant(sF2)
| spl3_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f119,plain,
( spl3_13
<=> constant(sF2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).
fof(f149,plain,
( spl3_16
| spl3_18
| ~ spl3_13
| spl3_12
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f106,f102,f115,f119,f142,f132]) ).
fof(f102,plain,
( spl3_11
<=> sF2 = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).
fof(f106,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| ~ constant(sF2)
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ spl3_11 ),
inference(superposition,[],[f27,f104]) ).
fof(f104,plain,
( sF2 = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f27,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| decreases(X1)
| constant(X1)
| increases(X1) ),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ constant(X0)
| constant(X1)
| decreases(X1)
| increases(X1)
| sum(X1,X2) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).
fof(f148,plain,
( spl3_16
| ~ spl3_13
| spl3_17
| spl3_18
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f111,f102,f142,f137,f119,f132]) ).
fof(f111,plain,
( increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| ~ constant(sF2)
| constant(cardinality_at_time(first_movers,sk2))
| ~ spl3_11 ),
inference(superposition,[],[f33,f104]) ).
fof(f33,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| increases(X1)
| increases(X2) ),
inference(equality_resolution,[],[f7]) ).
fof(f7,axiom,
! [X2,X0,X1] :
( sum(X1,X2) != X0
| increases(X2)
| increases(X1)
| ~ constant(X0)
| constant(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_33) ).
fof(f147,plain,
( spl3_17
| spl3_14
| spl3_18
| ~ spl3_13
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f112,f102,f119,f142,f123,f137]) ).
fof(f112,plain,
( ~ constant(sF2)
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| ~ spl3_11 ),
inference(superposition,[],[f34,f104]) ).
fof(f34,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| increases(X2)
| constant(X2)
| increases(X1) ),
inference(equality_resolution,[],[f11]) ).
fof(f11,axiom,
! [X2,X0,X1] :
( increases(X1)
| sum(X1,X2) != X0
| constant(X2)
| ~ constant(X0)
| increases(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).
fof(f146,plain,
( ~ spl3_13
| spl3_15
| spl3_17
| spl3_14
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f108,f102,f123,f137,f127,f119]) ).
fof(f108,plain,
( constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| ~ constant(sF2)
| ~ spl3_11 ),
inference(superposition,[],[f29,f104]) ).
fof(f29,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X2)
| decreases(X2)
| increases(X2) ),
inference(equality_resolution,[],[f13]) ).
fof(f13,axiom,
! [X2,X0,X1] :
( decreases(X2)
| constant(X2)
| increases(X2)
| sum(X1,X2) != X0
| ~ constant(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).
fof(f145,plain,
( spl3_18
| spl3_14
| ~ spl3_13
| spl3_12
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f107,f102,f115,f119,f123,f142]) ).
fof(f107,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| ~ constant(sF2)
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| ~ spl3_11 ),
inference(superposition,[],[f28,f104]) ).
fof(f28,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| increases(X1)
| decreases(X1)
| constant(X2) ),
inference(equality_resolution,[],[f10]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( increases(X1)
| decreases(X1)
| ~ constant(X0)
| constant(X2)
| sum(X1,X2) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).
fof(f140,plain,
( ~ spl3_13
| spl3_15
| spl3_16
| spl3_17
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f110,f102,f137,f132,f127,f119]) ).
fof(f110,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| ~ constant(sF2)
| ~ spl3_11 ),
inference(superposition,[],[f31,f104]) ).
fof(f31,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| constant(X1)
| decreases(X2)
| increases(X2) ),
inference(equality_resolution,[],[f9]) ).
fof(f9,axiom,
! [X2,X0,X1] :
( decreases(X2)
| sum(X1,X2) != X0
| increases(X2)
| ~ constant(X0)
| constant(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).
fof(f135,plain,
( spl3_16
| ~ spl3_13
| spl3_12
| spl3_15
| ~ spl3_11 ),
inference(avatar_split_clause,[],[f113,f102,f127,f115,f119,f132]) ).
fof(f113,plain,
( decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2))
| ~ constant(sF2)
| constant(cardinality_at_time(first_movers,sk2))
| ~ spl3_11 ),
inference(superposition,[],[f35,f104]) ).
fof(f35,plain,
! [X2,X1] :
( ~ constant(sum(X1,X2))
| decreases(X1)
| decreases(X2)
| constant(X1) ),
inference(equality_resolution,[],[f8]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( decreases(X1)
| sum(X1,X2) != X0
| ~ constant(X0)
| decreases(X2)
| constant(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_34) ).
fof(f105,plain,
( ~ spl3_7
| spl3_11
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f100,f77,f102,f73]) ).
fof(f100,plain,
( sF2 = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
| ~ environment(sk1)
| ~ spl3_8 ),
inference(forward_demodulation,[],[f99,f40]) ).
fof(f99,plain,
( number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))
| ~ environment(sk1)
| ~ spl3_8 ),
inference(resolution,[],[f98,f79]) ).
fof(f98,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1)) = number_of_organizations(X0,X1)
| ~ environment(X0) ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1)) = number_of_organizations(X0,X1)
| ~ environment(X0) ),
inference(resolution,[],[f32,f5]) ).
fof(f32,plain,
! [X2,X0] :
( ~ subpopulation(efficient_producers,X0,X2)
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ~ environment(X0) ),
inference(equality_resolution,[],[f2]) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ subpopulation(X1,X0,X2)
| number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ~ environment(X0)
| efficient_producers != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_28) ).
fof(f94,plain,
( spl3_10
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f89,f73,f91]) ).
fof(f89,plain,
( ~ environment(sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[],[f18,f22]) ).
fof(f22,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_48) ).
fof(f18,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).
fof(f88,plain,
( spl3_9
| ~ spl3_7 ),
inference(avatar_split_clause,[],[f83,f73,f85]) ).
fof(f83,plain,
( ~ environment(sk1)
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[],[f17,f22]) ).
fof(f17,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).
fof(f82,plain,
spl3_7,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f81,plain,
( $false
| spl3_7 ),
inference(resolution,[],[f75,f21]) ).
fof(f21,axiom,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_47) ).
fof(f75,plain,
( ~ environment(sk1)
| spl3_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f80,plain,
( ~ spl3_7
| spl3_8 ),
inference(avatar_split_clause,[],[f71,f77,f73]) ).
fof(f71,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[],[f19,f22]) ).
fof(f19,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_45) ).
fof(f70,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f42,f67,f63]) ).
fof(f42,plain,
( zero != sF0
| zero != sF1 ),
inference(definition_folding,[],[f24,f37,f38]) ).
fof(f24,axiom,
( zero != growth_rate(efficient_producers,sk2)
| zero != growth_rate(first_movers,sk2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_50) ).
fof(f61,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f39,f58,f54]) ).
fof(f39,plain,
( ~ greater(zero,sF0)
| ~ greater(sF1,zero) ),
inference(definition_folding,[],[f26,f38,f37]) ).
fof(f26,axiom,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_52) ).
fof(f52,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f43,f49,f45]) ).
fof(f43,plain,
( ~ greater(sF0,zero)
| ~ greater(zero,sF1) ),
inference(definition_folding,[],[f25,f37,f38]) ).
fof(f25,axiom,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_51) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : MGT025-1 : TPTP v8.1.0. Released v2.4.0.
% 0.09/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 03:16:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.49 % (17715)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.18/0.50 % (17701)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50 % (17701)First to succeed.
% 0.18/0.50 % (17702)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.50 % (17703)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.50 % (17701)Refutation found. Thanks to Tanya!
% 0.18/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50 % (17701)------------------------------
% 0.18/0.50 % (17701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50 % (17701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50 % (17701)Termination reason: Refutation
% 0.18/0.50
% 0.18/0.50 % (17701)Memory used [KB]: 5500
% 0.18/0.50 % (17701)Time elapsed: 0.110 s
% 0.18/0.50 % (17701)Instructions burned: 4 (million)
% 0.18/0.50 % (17701)------------------------------
% 0.18/0.50 % (17701)------------------------------
% 0.18/0.50 % (17688)Success in time 0.158 s
%------------------------------------------------------------------------------