%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT027-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 : Thu Sep 24 01:25:19 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 36
% Syntax : Number of formulae : 134 ( 7 unt; 21 def)
% Number of atoms : 449 ( 6 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 606 ( 291 ~; 294 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 22 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( contracts_from(B,first_movers)
| greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( contracts_from(B,first_movers)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( contracts_from(B,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( in_environment(A,C)
| ~ greater(C,B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( in_environment(A,appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [A] :
( greater(sk2(A),appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [A,B] :
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [A] :
( ~ contracts_from(A,first_movers)
| ~ greater(A,appear(efficient_producers,sk3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [B] :
( contracts_from(B,first_movers)
| ! [A] :
( greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sk1(X1,X0)),zero)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [B] :
( contracts_from(B,first_movers)
| ! [A] :
( greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| greater_or_equal(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [B] :
( contracts_from(B,first_movers)
| ! [A] :
( ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] :
( contracts_from(X1,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [A,C] :
( in_environment(A,C)
| ! [B] :
( ~ greater(C,B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0,X1,X2] :
( in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [A,C] :
( greater(A,C)
| ! [B] :
( ~ greater(B,C)
| ~ greater(A,B) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
! [B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ! [A] :
( ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,B)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f33,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0] :
( greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f35,plain,
! [B] :
( greater(zero,growth_rate(first_movers,B))
| ! [A] :
( ~ greater_or_equal(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
environment(sk3),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
stable(sk3),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
! [X0] :
( ~ contracts_from(X0,first_movers)
| ~ greater(X0,appear(efficient_producers,sk3)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f46,plain,
( greater(sk2(sk3),appear(efficient_producers,sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[f34,f37]) ).
fof(f47,definition,
( sQ0_spl
<=> stable(sk3) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ0_spl
| ~ stable(sk3) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ1_spl
<=> greater(sk2(sk3),appear(efficient_producers,sk3)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ1_spl
| greater(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f47,f50]) ).
fof(f54,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f38]) ).
fof(f55,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f54]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ contracts_from(sk2(sk3),first_movers) ),
inference(resolution,[status(thm)],[f51,f39]) ).
fof(f57,plain,
( ~ sQ1_spl
| greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[f51,f30]) ).
fof(f58,plain,
! [X0] :
( ~ sQ1_spl
| greater(X0,appear(efficient_producers,sk3))
| ~ greater(X0,sk2(sk3)) ),
inference(resolution,[status(thm)],[f51,f28]) ).
fof(f59,plain,
! [X0] :
( ~ sQ1_spl
| greater_or_equal(sk1(sk2(sk3),X0),sk2(sk3))
| ~ in_environment(X0,sk2(sk3))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f56,f20]) ).
fof(f60,plain,
! [X0] :
( ~ sQ1_spl
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),X0)),zero)
| ~ in_environment(X0,sk2(sk3))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f56,f18]) ).
fof(f61,plain,
( ~ sQ1_spl
| greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ in_environment(sk3,sk2(sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f57,f33]) ).
fof(f63,definition,
( sQ2_spl
<=> environment(sk3) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ2_spl
| ~ environment(sk3) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ3_spl
<=> in_environment(sk3,sk2(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ3_spl
| in_environment(sk3,sk2(sk3)) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ3_spl
| ~ in_environment(sk3,sk2(sk3)) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ4_spl
<=> greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ1_spl
| sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f61,f63,f66,f69,f50]) ).
fof(f84,plain,
! [X0] :
( ~ sQ1_spl
| sk1(sk2(sk3),X0) = sk2(sk3)
| greater(sk1(sk2(sk3),X0),sk2(sk3))
| ~ in_environment(X0,sk2(sk3))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f59,f29]) ).
fof(f85,plain,
( ~ sQ1_spl
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[f60,f37]) ).
fof(f86,definition,
( sQ7_spl
<=> greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ7_spl
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( ~ sQ1_spl
| sQ7_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f47,f66,f86,f50]) ).
fof(f90,plain,
! [X0] :
( sQ3_spl
| ~ greater(sk2(sk3),X0)
| ~ in_environment(sk3,X0)
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f68,f25]) ).
fof(f91,definition,
! [X0] :
( sQ8_spl
<=> ( ~ greater(sk2(sk3),X0)
| ~ in_environment(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f92,plain,
! [X0] :
( ~ sQ8_spl
| ~ greater(sk2(sk3),X0)
| ~ in_environment(sk3,X0) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ3_spl
| sQ8_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f90,f63,f47,f91,f66]) ).
fof(f95,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f37]) ).
fof(f96,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f95]) ).
fof(f97,plain,
( ~ sQ1_spl
| sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3) ),
inference(resolution,[status(thm)],[f84,f37]) ).
fof(f98,definition,
( sQ9_spl
<=> greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( ~ sQ9_spl
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,definition,
( sQ10_spl
<=> sk1(sk2(sk3),sk3) = sk2(sk3) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ10_spl
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( ~ sQ1_spl
| sQ10_spl
| sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f47,f66,f98,f101,f50]) ).
fof(f105,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ in_environment(sk3,appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[f92,f51]) ).
fof(f106,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f105,f26]) ).
fof(f108,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f106,f63,f47,f91,f50]) ).
fof(f117,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[f99,f58]) ).
fof(f122,plain,
! [X0] :
( ~ sQ7_spl
| subpopulations(first_movers,efficient_producers,X0,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(X0,sk1(sk2(sk3),sk3))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f87,f23]) ).
fof(f125,definition,
! [X0] :
( sQ12_spl
<=> ( subpopulations(first_movers,efficient_producers,X0,sk1(sk2(sk3),sk3))
| ~ in_environment(X0,sk1(sk2(sk3),sk3))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f126,plain,
! [X0] :
( ~ sQ12_spl
| subpopulations(first_movers,efficient_producers,X0,sk1(sk2(sk3),sk3))
| ~ in_environment(X0,sk1(sk2(sk3),sk3))
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
( sQ13_spl
<=> greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f122,f125,f128,f86]) ).
fof(f133,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[f117,f30]) ).
fof(f142,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f133,f33]) ).
fof(f144,definition,
( sQ15_spl
<=> in_environment(sk3,sk1(sk2(sk3),sk3)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ15_spl
| ~ in_environment(sk3,sk1(sk2(sk3),sk3)) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| sQ13_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f142,f63,f144,f128,f98,f50]) ).
fof(f155,plain,
! [X0] :
( sQ15_spl
| ~ greater(sk1(sk2(sk3),sk3),X0)
| ~ in_environment(sk3,X0)
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f146,f25]) ).
fof(f156,definition,
! [X0] :
( sQ18_spl
<=> ( ~ greater(sk1(sk2(sk3),sk3),X0)
| ~ in_environment(sk3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f157,plain,
! [X0] :
( ~ sQ18_spl
| ~ greater(sk1(sk2(sk3),sk3),X0)
| ~ in_environment(sk3,X0) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( sQ15_spl
| sQ18_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f155,f63,f47,f156,f144]) ).
fof(f161,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| ~ in_environment(sk3,sk2(sk3)) ),
inference(resolution,[status(thm)],[f157,f99]) ).
fof(f162,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f161,f66,f156,f98]) ).
fof(f170,plain,
( ~ sQ12_spl
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| ~ in_environment(sk3,sk1(sk2(sk3),sk3)) ),
inference(resolution,[status(thm)],[f126,f37]) ).
fof(f171,definition,
( sQ20_spl
<=> subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ20_spl
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( ~ sQ12_spl
| sQ20_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f170,f144,f171,f125]) ).
fof(f178,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| greater(cardinality_at_time(first_movers,sk2(sk3)),zero) ),
inference(backward_demodulation,[status(thm)],[f102,f87]) ).
fof(f179,plain,
( ~ sQ10_spl
| ~ sQ1_spl
| greater_or_equal(sk2(sk3),sk2(sk3))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(paramodulation,[status(thm)],[f102,f59]) ).
fof(f180,plain,
( ~ sQ10_spl
| contracts_from(sk2(sk3),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(paramodulation,[status(thm)],[f102,f22]) ).
fof(f182,definition,
( sQ21_spl
<=> greater_or_equal(sk2(sk3),sk2(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ10_spl
| ~ sQ1_spl
| sQ21_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f179,f63,f47,f66,f182,f50,f101]) ).
fof(f186,definition,
( sQ22_spl
<=> greater(zero,growth_rate(first_movers,sk2(sk3))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f189,definition,
( sQ23_spl
<=> contracts_from(sk2(sk3),first_movers) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ23_spl
| contracts_from(sk2(sk3),first_movers) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ10_spl
| sQ23_spl
| ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f180,f63,f47,f66,f186,f189,f101]) ).
fof(f193,plain,
( sQ15_spl
| ~ sQ10_spl
| ~ in_environment(sk3,sk2(sk3)) ),
inference(forward_demodulation,[status(thm)],[f102,f146]) ).
fof(f194,plain,
( sQ15_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f193,f67]) ).
fof(f195,plain,
( sQ15_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f209,plain,
( ~ sQ20_spl
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f172,f36]) ).
fof(f210,definition,
( sQ24_spl
<=> greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ24_spl
| ~ greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,definition,
( sQ25_spl
<=> greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ25_spl
| greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( ~ sQ20_spl
| sQ25_spl
| ~ sQ24_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f209,f63,f47,f210,f213,f171]) ).
fof(f235,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ10_spl
| subpopulations(first_movers,efficient_producers,X0,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ in_environment(X0,sk2(sk3))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f178,f23]) ).
fof(f238,definition,
! [X0] :
( sQ28_spl
<=> ( subpopulations(first_movers,efficient_producers,X0,sk2(sk3))
| ~ in_environment(X0,sk2(sk3))
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0] :
( ~ sQ28_spl
| subpopulations(first_movers,efficient_producers,X0,sk2(sk3))
| ~ in_environment(X0,sk2(sk3))
| ~ environment(X0) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ4_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f235,f238,f69,f101,f86]) ).
fof(f252,plain,
( ~ sQ1_spl
| sQ24_spl
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f212,f59]) ).
fof(f253,plain,
( ~ sQ1_spl
| sQ24_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f252,f63,f47,f66,f210,f50]) ).
fof(f274,plain,
( ~ sQ25_spl
| contracts_from(sk2(sk3),first_movers)
| ~ in_environment(sk3,sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f214,f22]) ).
fof(f277,plain,
( ~ sQ25_spl
| sQ23_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f274,f63,f47,f66,f189,f213]) ).
fof(f278,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f56]) ).
fof(f279,plain,
( ~ sQ23_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f303,plain,
( ~ sQ28_spl
| subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| ~ in_environment(sk3,sk2(sk3)) ),
inference(resolution,[status(thm)],[f239,f37]) ).
fof(f304,definition,
( sQ30_spl
<=> subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( ~ sQ30_spl
| subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,plain,
( ~ sQ28_spl
| sQ30_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f303,f66,f304,f238]) ).
fof(f308,plain,
( ~ sQ30_spl
| greater(zero,growth_rate(first_movers,sk2(sk3)))
| ~ greater_or_equal(sk2(sk3),sk2(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(resolution,[status(thm)],[f305,f36]) ).
fof(f309,plain,
( ~ sQ30_spl
| sQ22_spl
| ~ sQ21_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f308,f63,f47,f182,f186,f304]) ).
fof(f310,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f55,f72,f89,f94,f96,f104,f108,f131,f147,f159,f162,f174,f185,f192,f195,f216,f241,f253,f277,f279,f307,f309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT027-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n014.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 01:22:21 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.053971 seconds
% 0.14/0.42 % CPU time: 0.177208 seconds
% 0.14/0.42 % Total memory used: 81.369 MB
% 0.14/0.42 % Net memory used: 80.952 MB
%------------------------------------------------------------------------------