%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT022+2 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 94 ( 37 ~; 33 |; 13 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a6,hypothesis,
! [X2,X3,X4,X5] :
( ( environment(X2)
& subpopulations(X3,X4,X2,X5)
& greater(resilience(X4),resilience(X3)) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(X3,X5),disbanding_rate(X4,X5))) )
& ( constant(resources(X2,X5))
=> constant(difference(disbanding_rate(X3,X5),disbanding_rate(X4,X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6) ).
fof(prove_l4,conjecture,
! [X2,X5] :
( ( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X5) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) )
& ( constant(resources(X2,X5))
=> ~ decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4) ).
fof(mp_constant_not_decrease,axiom,
! [X1] :
( constant(X1)
=> ~ decreases(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(c_0_4,hypothesis,
! [X14,X15,X16,X17] :
( ( ~ decreases(resources(X14,X17))
| increases(difference(disbanding_rate(X15,X17),disbanding_rate(X16,X17)))
| ~ environment(X14)
| ~ subpopulations(X15,X16,X14,X17)
| ~ greater(resilience(X16),resilience(X15)) )
& ( ~ constant(resources(X14,X17))
| constant(difference(disbanding_rate(X15,X17),disbanding_rate(X16,X17)))
| ~ environment(X14)
| ~ subpopulations(X15,X16,X14,X17)
| ~ greater(resilience(X16),resilience(X15)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a6])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X2,X5] :
( ( environment(X2)
& subpopulations(first_movers,efficient_producers,X2,X5) )
=> ( ( decreases(resources(X2,X5))
=> increases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) )
& ( constant(resources(X2,X5))
=> ~ decreases(difference(disbanding_rate(first_movers,X5),disbanding_rate(efficient_producers,X5))) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_l4])]) ).
fof(c_0_6,plain,
! [X1] :
( constant(X1)
=> ~ decreases(X1) ),
inference(fof_simplification,[status(thm)],[mp_constant_not_decrease]) ).
cnf(c_0_7,hypothesis,
( constant(difference(disbanding_rate(X3,X2),disbanding_rate(X4,X2)))
| ~ constant(resources(X1,X2))
| ~ environment(X1)
| ~ subpopulations(X3,X4,X1,X2)
| ~ greater(resilience(X4),resilience(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
fof(c_0_9,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& ( constant(resources(esk1_0,esk2_0))
| decreases(resources(esk1_0,esk2_0)) )
& ( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| decreases(resources(esk1_0,esk2_0)) )
& ( constant(resources(esk1_0,esk2_0))
| ~ increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) )
& ( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10,plain,
! [X13] :
( ~ constant(X13)
| ~ decreases(X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_11,hypothesis,
( constant(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| ~ constant(resources(X2,X1)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ constant(X1)
| ~ decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( constant(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ constant(resources(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_16,hypothesis,
( increases(difference(disbanding_rate(X3,X2),disbanding_rate(X4,X2)))
| ~ decreases(resources(X1,X2))
| ~ environment(X1)
| ~ subpopulations(X3,X4,X1,X2)
| ~ greater(resilience(X4),resilience(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
( ~ decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| ~ constant(resources(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0)))
| decreases(resources(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( constant(resources(esk1_0,esk2_0))
| decreases(resources(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,hypothesis,
( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| ~ decreases(resources(X2,X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_8]) ).
cnf(c_0_21,negated_conjecture,
decreases(resources(esk1_0,esk2_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( constant(resources(esk1_0,esk2_0))
| ~ increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_23,negated_conjecture,
increases(difference(disbanding_rate(first_movers,esk2_0),disbanding_rate(efficient_producers,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_13])]),c_0_21])]) ).
cnf(c_0_24,negated_conjecture,
constant(resources(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_24]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT022+2 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n018.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 23:26:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------