%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT021+1 : 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 : n009.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 04:47:08 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 6 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 143 ( 59 ~; 48 |; 18 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a3,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(number_of_organizations(X1,X2),zero) )
=> ( ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) )
& ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(l4,hypothesis,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
& ( constant(resources(X1,X2))
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
fof(prove_l3,conjecture,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3) ).
fof(mp_environment_not_empty,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> greater(number_of_organizations(X1,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty) ).
fof(mp_time_point_in_environment,axiom,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment) ).
fof(mp_increase_not_decrease,axiom,
! [X3] :
( increases(X3)
=> ~ decreases(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease) ).
fof(c_0_6,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(number_of_organizations(X1,X2),zero) )
=> ( ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) )
& ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_7,hypothesis,
! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) )
& ( constant(resources(X1,X2))
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ) ) ),
inference(fof_simplification,[status(thm)],[l4]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_l3])]) ).
fof(c_0_9,hypothesis,
! [X25,X26] :
( ( ~ greater(equilibrium(X25),X26)
| decreases(resources(X25,X26))
| ~ environment(X25)
| ~ in_environment(X25,X26)
| ~ greater(number_of_organizations(X25,X26),zero) )
& ( greater(equilibrium(X25),X26)
| constant(resources(X25,X26))
| ~ environment(X25)
| ~ in_environment(X25,X26)
| ~ greater(number_of_organizations(X25,X26),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X20,X21] :
( ~ environment(X20)
| ~ subpopulations(first_movers,efficient_producers,X20,X21)
| greater(number_of_organizations(X20,X21),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_not_empty])]) ).
fof(c_0_11,plain,
! [X18,X19] :
( ~ environment(X18)
| ~ subpopulations(first_movers,efficient_producers,X18,X19)
| in_environment(X18,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_in_environment])]) ).
fof(c_0_12,hypothesis,
! [X27,X28] :
( ( ~ decreases(resources(X27,X28))
| increases(difference(disbanding_rate(first_movers,X28),disbanding_rate(efficient_producers,X28)))
| ~ environment(X27)
| ~ subpopulations(first_movers,efficient_producers,X27,X28) )
& ( ~ constant(resources(X27,X28))
| ~ decreases(difference(disbanding_rate(first_movers,X28),disbanding_rate(efficient_producers,X28)))
| ~ environment(X27)
| ~ subpopulations(first_movers,efficient_producers,X27,X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_13,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_14,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X3] :
( increases(X3)
=> ~ decreases(X3) ),
inference(fof_simplification,[status(thm)],[mp_increase_not_decrease]) ).
cnf(c_0_18,hypothesis,
( ~ constant(resources(X1,X2))
| ~ decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,hypothesis,
( constant(resources(X1,X2))
| greater(equilibrium(X1),X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_23,plain,
! [X22] :
( ~ increases(X22)
| ~ decreases(X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
cnf(c_0_24,hypothesis,
( increases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ decreases(resources(X1,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,hypothesis,
( decreases(resources(X1,X2))
| ~ greater(equilibrium(X1),X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,negated_conjecture,
( ~ constant(resources(X1,esk2_0))
| ~ subpopulations(first_movers,efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( constant(resources(esk1_0,esk2_0))
| greater(equilibrium(esk1_0),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_28,plain,
( ~ increases(X1)
| ~ decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
( increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ decreases(resources(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_22])]) ).
cnf(c_0_30,hypothesis,
( decreases(resources(X1,X2))
| ~ greater(equilibrium(X1),X2)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_16]) ).
cnf(c_0_31,negated_conjecture,
greater(equilibrium(esk1_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21]),c_0_22])]) ).
cnf(c_0_32,negated_conjecture,
~ decreases(resources(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19])]) ).
cnf(c_0_33,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21]),c_0_22])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT021+1 : 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
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:26:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------