%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT036+3 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 5 04:48:15 PM UTC 2026
% Result : Theorem 0.28s 1.63s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 89 ( 37 ~; 34 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t5_star,conjecture,
? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& outcompetes(first_movers,efficient_producers,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_star) ).
fof(mp_symmetry_of_subpopulations,axiom,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> subpopulations(X3,X2,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(d2,hypothesis,
! [X1,X2,X3,X4] :
( ( environment(X1)
& subpopulations(X2,X3,X1,X4) )
=> ( ( greater_or_equal(growth_rate(X3,X4),zero)
& greater(zero,growth_rate(X2,X4)) )
<=> outcompetes(X3,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(a13_star,hypothesis,
? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& greater_or_equal(growth_rate(first_movers,X4),zero)
& greater(zero,growth_rate(efficient_producers,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star) ).
fof(i_0_4,negated_conjecture,
~ ? [X1,X4] :
( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X4)
& outcompetes(first_movers,efficient_producers,X4) ),
inference(assume_negation,[status(cth)],[prove_t5_star]) ).
fof(i_0_5,plain,
! [X17,X18,X19,X20] :
( ~ environment(X17)
| ~ subpopulations(X18,X19,X17,X20)
| subpopulations(X19,X18,X17,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_symmetry_of_subpopulations])]) ).
fof(i_0_6,hypothesis,
! [X21,X22,X23,X24] :
( ( ~ greater_or_equal(growth_rate(X23,X24),zero)
| ~ greater(zero,growth_rate(X22,X24))
| outcompetes(X23,X22,X24)
| ~ environment(X21)
| ~ subpopulations(X22,X23,X21,X24) )
& ( greater_or_equal(growth_rate(X23,X24),zero)
| ~ outcompetes(X23,X22,X24)
| ~ environment(X21)
| ~ subpopulations(X22,X23,X21,X24) )
& ( greater(zero,growth_rate(X22,X24))
| ~ outcompetes(X23,X22,X24)
| ~ environment(X21)
| ~ subpopulations(X22,X23,X21,X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2])])]) ).
fof(i_0_7,negated_conjecture,
! [X27,X28] :
( ~ environment(X27)
| ~ subpopulations(first_movers,efficient_producers,X27,X28)
| ~ outcompetes(first_movers,efficient_producers,X28) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_4])]) ).
fof(i_0_8,hypothesis,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& greater_or_equal(growth_rate(first_movers,esk2_0),zero)
& greater(zero,growth_rate(efficient_producers,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[a13_star])]) ).
cnf(i_0_9,plain,
( subpopulations(X3,X2,X1,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_10,hypothesis,
( outcompetes(X1,X3,X2)
| ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X3,X2))
| ~ environment(X4)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_11,hypothesis,
( greater_or_equal(growth_rate(X1,X2),zero)
| ~ outcompetes(X1,X3,X2)
| ~ environment(X4)
| ~ subpopulations(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_12,hypothesis,
( greater(zero,growth_rate(X1,X2))
| ~ outcompetes(X3,X1,X2)
| ~ environment(X4)
| ~ subpopulations(X1,X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_13,negated_conjecture,
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ outcompetes(first_movers,efficient_producers,X2) ),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_14,hypothesis,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_15,hypothesis,
greater_or_equal(growth_rate(first_movers,esk2_0),zero),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_16,hypothesis,
greater(zero,growth_rate(efficient_producers,esk2_0)),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_17,hypothesis,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_18,plain,
subpopulations(efficient_producers,first_movers,esk1_0,esk2_0),
inference(scs_inference,[],[i_0_14,i_0_17,i_0_9]) ).
cnf(i_0_19,plain,
( ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| subpopulations(X3,X2,X1,X4) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_20,plain,
outcompetes(first_movers,efficient_producers,esk2_0),
inference(scs_inference,[],[i_0_14,i_0_17,i_0_15,i_0_16,i_0_9,i_0_10]) ).
cnf(i_0_21,plain,
( ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X3,X2))
| ~ subpopulations(X3,X1,X4,X2)
| outcompetes(X1,X3,X2)
| ~ environment(X4) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_22,plain,
$false,
inference(scs_inference,[],[i_0_14,i_0_17,i_0_15,i_0_16,i_0_9,i_0_10,i_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+3 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 23:29:10 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 0.28/1.63 % Version : CSE_E---1.7
% 0.28/1.63 % Problem : theBenchmark.p
% 0.28/1.63 % SZS status Theorem for theBenchmark.p
% 0.28/1.63 % SZS output start CNFRefutation
% See solution above
% 0.28/1.65 % Total time : 1.273s
%------------------------------------------------------------------------------