TSTP Solution File: MGT023+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : MGT023+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 : Tue May 21 00:41:46 EDT 2024
% Result : Theorem 23.01s 4.32s
% Output : Refutation 23.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 11 unt; 12 typ; 0 def)
% Number of atoms : 186 ( 32 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 746 ( 81 ~; 91 |; 19 &; 544 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-4 aty)
% Number of variables : 43 ( 0 ^ 41 !; 2 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(environment_type,type,
environment: $i > $o ).
thf(stable_type,type,
stable: $i > $o ).
thf(in_environment_type,type,
in_environment: $i > $i > $o ).
thf(critical_point_type,type,
critical_point: $i > $i ).
thf(greater_type,type,
greater: $i > $i > $o ).
thf(growth_rate_type,type,
growth_rate: $i > $i > $i ).
thf(efficient_producers_type,type,
efficient_producers: $i ).
thf(first_movers_type,type,
first_movers: $i ).
thf(subpopulations_type,type,
subpopulations: $i > $i > $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(1,conjecture,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ( in_environment @ A @ ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ( in_environment @ A @ ( critical_point @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ( in_environment @ A @ ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
stable @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(4,axiom,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
thf(16,plain,
! [A: $i] :
( ( ( environment @ A )
& ( stable @ A ) )
=> ? [B: $i] :
( ( in_environment @ A @ B )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( in_environment @ A @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(21,plain,
! [A: $i] :
( ~ ( environment @ A )
| ( in_environment @ A @ ( sk3 @ A ) )
| ( ( stable @ sk1 )
!= ( stable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,17]) ).
thf(22,plain,
( ~ ( environment @ sk1 )
| ( in_environment @ sk1 @ ( sk3 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk1 ))]]) ).
thf(8,plain,
environment @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(88,plain,
( ~ $true
| ( in_environment @ sk1 @ ( sk3 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[22,8]) ).
thf(89,plain,
in_environment @ sk1 @ ( sk3 @ sk1 ),
inference(simp,[status(thm)],[88]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) )
=> ( B
= ( critical_point @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(9,plain,
! [A: $i,B: $i] :
( ( ( environment @ A )
& ~ ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
& ( in_environment @ A @ B )
& ! [C: $i] :
( ( ( subpopulations @ first_movers @ efficient_producers @ A @ C )
& ( greater @ C @ B ) )
=> ( greater @ ( growth_rate @ efficient_producers @ C ) @ ( growth_rate @ first_movers @ C ) ) ) )
=> ( B
= ( critical_point @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk2 @ B @ A ) )
| ( B
= ( critical_point @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B
= ( critical_point @ A ) )
| ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk2 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(706,plain,
! [B: $i,A: $i] :
( ( B
= ( critical_point @ A ) )
| ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ( subpopulations @ first_movers @ efficient_producers @ A @ ( sk2 @ B @ A ) )
| ( ( in_environment @ sk1 @ ( sk3 @ sk1 ) )
!= ( in_environment @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,15]) ).
thf(707,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ~ ( environment @ sk1 )
| ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk3 @ sk1 ) ) )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[706:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(18,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ A ) ) @ ( growth_rate @ first_movers @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(29,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ A ) ) @ ( growth_rate @ first_movers @ ( sk3 @ A ) ) )
| ( ( stable @ sk1 )
!= ( stable @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,18]) ).
thf(30,plain,
( ~ ( environment @ sk1 )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk3 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 ))]]) ).
thf(221,plain,
( ~ $true
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk3 @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[30,8]) ).
thf(222,plain,
~ ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(1540,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ~ $true
| $false
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) ),
inference(rewrite,[status(thm)],[707,8,222]) ).
thf(1541,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[1540]) ).
thf(6,plain,
~ ( in_environment @ sk1 @ ( critical_point @ sk1 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(20,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( ( in_environment @ A @ ( sk3 @ A ) )
!= ( in_environment @ sk1 @ ( critical_point @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,6]) ).
thf(25,plain,
! [A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ( A != sk1 )
| ( ( sk3 @ A )
!= ( critical_point @ sk1 ) ) ),
inference(simp,[status(thm)],[20]) ).
thf(26,plain,
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ( ( sk3 @ sk1 )
!= ( critical_point @ sk1 ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
( ~ $true
| ~ $true
| ( ( sk3 @ sk1 )
!= ( critical_point @ sk1 ) ) ),
inference(rewrite,[status(thm)],[26,7,8]) ).
thf(28,plain,
( ( sk3 @ sk1 )
!= ( critical_point @ sk1 ) ),
inference(simp,[status(thm)],[27]) ).
thf(1542,plain,
subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ),
inference(simplifyReflect,[status(thm)],[1541,28]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( subpopulations @ first_movers @ efficient_producers @ A @ B )
| ~ ( greater @ B @ ( sk3 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ~ ( stable @ A )
| ~ ( greater @ B @ ( sk3 @ A ) )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ( ( subpopulations @ first_movers @ efficient_producers @ sk1 @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) )
!= ( subpopulations @ first_movers @ efficient_producers @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1542,19]) ).
thf(1553,plain,
( ~ ( environment @ sk1 )
| ~ ( stable @ sk1 )
| ~ ( greater @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) @ ( sk3 @ sk1 ) )
| ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1552:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ ( sk3 @ sk1 ) @ sk1 ))]]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( greater @ ( sk2 @ B @ A ) @ B )
| ( B
= ( critical_point @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B
= ( critical_point @ A ) )
| ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( greater @ ( sk2 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( B
= ( critical_point @ A ) )
| ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ( greater @ ( sk2 @ B @ A ) @ B )
| ( ( in_environment @ sk1 @ ( sk3 @ sk1 ) )
!= ( in_environment @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,14]) ).
thf(91,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ~ ( environment @ sk1 )
| ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk3 @ sk1 ) ) )
| ( greater @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) @ ( sk3 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(256,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ~ $true
| $false
| ( greater @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) @ ( sk3 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[91,8,222]) ).
thf(257,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ( greater @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) @ ( sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
greater @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) @ ( sk3 @ sk1 ),
inference(simplifyReflect,[status(thm)],[257,28]) ).
thf(3126,plain,
( ~ $true
| ~ $true
| ~ $true
| ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) ) ),
inference(rewrite,[status(thm)],[1553,258,7,8]) ).
thf(3127,plain,
greater @ ( growth_rate @ efficient_producers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[3126]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ B @ A ) ) )
| ( B
= ( critical_point @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( B
= ( critical_point @ A ) )
| ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ~ ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ B @ A ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(3175,plain,
! [B: $i,A: $i] :
( ( B
= ( critical_point @ A ) )
| ~ ( environment @ A )
| ( greater @ ( growth_rate @ efficient_producers @ B ) @ ( growth_rate @ first_movers @ B ) )
| ~ ( in_environment @ A @ B )
| ( ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk2 @ ( sk3 @ sk1 ) @ sk1 ) ) )
!= ( greater @ ( growth_rate @ efficient_producers @ ( sk2 @ B @ A ) ) @ ( growth_rate @ first_movers @ ( sk2 @ B @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[3127,13]) ).
thf(3176,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ~ ( environment @ sk1 )
| ( greater @ ( growth_rate @ efficient_producers @ ( sk3 @ sk1 ) ) @ ( growth_rate @ first_movers @ ( sk3 @ sk1 ) ) )
| ~ ( in_environment @ sk1 @ ( sk3 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3175:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(3511,plain,
( ( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) )
| ~ $true
| $false
| ~ $true ),
inference(rewrite,[status(thm)],[3176,8,89,222]) ).
thf(3512,plain,
( ( sk3 @ sk1 )
= ( critical_point @ sk1 ) ),
inference(simp,[status(thm)],[3511]) ).
thf(3513,plain,
$false,
inference(simplifyReflect,[status(thm)],[3512,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : MGT023+1 : TPTP v8.2.0. Released v2.0.0.
% 0.08/0.10 % Command : run_Leo-III %s %d
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Sun May 19 00:02:09 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.62/0.66 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.76 % [INFO] Parsing done (93ms).
% 0.91/0.76 % [INFO] Running in sequential loop mode.
% 1.13/0.96 % [INFO] nitpick registered as external prover.
% 1.13/0.97 % [INFO] Scanning for conjecture ...
% 1.29/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.29/1.04 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.29/1.05 % [INFO] Problem is first-order (TPTP FOF).
% 1.29/1.06 % [INFO] Type checking passed.
% 1.29/1.06 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 23.01/4.31 % [INFO] Killing All external provers ...
% 23.01/4.32 % Time passed: 3930ms (effective reasoning time: 3549ms)
% 23.01/4.32 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 23.01/4.32 % Axioms used in derivation (2): l12, d1
% 23.01/4.32 % No. of inferences in proof: 51
% 23.01/4.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3930 ms resp. 3549 ms w/o parsing
% 23.05/4.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.05/4.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------