%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:50:36 AM UTC 2026
% Result : Theorem 0.14s 5.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 28 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 147 ( 57 ~; 49 |; 31 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 19 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_constant_not_decrease,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('theBenchmark.p',mp_constant_not_decrease) ).
fof(a6,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('theBenchmark.p',a6) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2) ).
fof(prove_l4,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('theBenchmark.p',prove_l4) ).
fof(f_1_1,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(fof_nnf,[status(thm)],[mp_constant_not_decrease]) ).
fof(f_1_2,plain,
! [U_0] :
( ~ decreases(U_0)
| ~ constant(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
( ~ decreases(U_0)
| ~ constant(U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [E,S1,S2,T] :
( ( ( constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ constant(resources(E,T)) )
& ( increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ decreases(resources(E,T)) ) )
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[a6]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2,U_1] :
( ( ( constant(difference(disbanding_rate(U_3,U_1),disbanding_rate(U_2,U_1)))
| ~ constant(resources(U_4,U_1)) )
& ( increases(difference(disbanding_rate(U_3,U_1),disbanding_rate(U_2,U_1)))
| ~ decreases(resources(U_4,U_1)) ) )
| ~ greater(resilience(U_2),resilience(U_3))
| ~ subpopulations(U_3,U_2,U_4,U_1)
| ~ environment(U_4) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( increases(difference(disbanding_rate(U_3,U_1),disbanding_rate(U_2,U_1)))
| ~ decreases(resources(U_4,U_1))
| ~ greater(resilience(U_2),resilience(U_3))
| ~ subpopulations(U_3,U_2,U_4,U_1)
| ~ environment(U_4) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( constant(difference(disbanding_rate(U_3,U_1),disbanding_rate(U_2,U_1)))
| ~ constant(resources(U_4,U_1))
| ~ greater(resilience(U_2),resilience(U_3))
| ~ subpopulations(U_3,U_2,U_4,U_1)
| ~ environment(U_4) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(fof_nnf,[status(thm)],[a2]) ).
cnf(f_3_2,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
inference(negate,[status(cth)],[prove_l4]) ).
fof(f_4_2,negated_conjecture,
? [E,T] :
( ( ( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& constant(resources(E,T)) )
| ( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T)) ) )
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_6,U_5] :
( ( ( decreases(difference(disbanding_rate(first_movers,U_5),disbanding_rate(efficient_producers,U_5)))
& constant(resources(U_6,U_5)) )
| ( ~ increases(difference(disbanding_rate(first_movers,U_5),disbanding_rate(efficient_producers,U_5)))
& decreases(resources(U_6,U_5)) ) )
& subpopulations(first_movers,efficient_producers,U_6,U_5)
& environment(U_6) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_5] :
( ( ( decreases(difference(disbanding_rate(first_movers,U_5),disbanding_rate(efficient_producers,U_5)))
& constant(resources(sK1,U_5)) )
| ( ~ increases(difference(disbanding_rate(first_movers,U_5),disbanding_rate(efficient_producers,U_5)))
& decreases(resources(sK1,U_5)) ) )
& subpopulations(first_movers,efficient_producers,sK1,U_5)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
( ( ( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
& constant(resources(sK1,sK2)) )
| ( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
& decreases(resources(sK1,sK2)) ) )
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( ( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP1 )
& ( constant(resources(sK1,sK2))
| ~ sP1 )
& ( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP0 )
& ( decreases(resources(sK1,sK2))
| ~ sP0 )
& ( sP1
| sP0 )
& subpopulations(first_movers,efficient_producers,sK1,sK2)
& environment(sK1) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_4_5]) ).
cnf(f_4_7,negated_conjecture,
environment(sK1),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_8,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_9,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_10,negated_conjecture,
( decreases(resources(sK1,sK2))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_11,negated_conjecture,
( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_12,negated_conjecture,
( constant(resources(sK1,sK2))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_13,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(t1,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP0 ),
inference(start,[status(thm),parent(0:0)],[f_4_11]) ).
cnf(t2,plain,
( sP1
| sP0 ),
inference(extension,[status(thm),parent(t1:1)],[f_4_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP1 ),
inference(extension,[status(thm),parent(t2:2)],[f_4_13]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(extension,[status(thm),parent(t4:2)],[f_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ constant(resources(sK1,sK2))
| ~ environment(sK1)
| constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(extension,[status(thm),parent(t6:2)],[f_2_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
environment(sK1),
inference(extension,[status(thm),parent(t8:2)],[f_4_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ sP1
| constant(resources(sK1,sK2)) ),
inference(extension,[status(thm),parent(t8:3)],[f_4_12]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
$false,
inference(reduction,[status(thm),parent(t12:2)],[t12:2,t2:2]) ).
cnf(t15,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(extension,[status(thm),parent(t8:4)],[f_3_2]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t8:4]) ).
cnf(t17,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t8:5)],[f_4_8]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t8:5]) ).
cnf(l1,lemma,
sP0,
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t19,plain,
( ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ decreases(resources(sK1,sK2))
| ~ environment(sK1)
| increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(extension,[status(thm),parent(t1:2)],[f_2_3]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t1:2]) ).
cnf(t21,plain,
environment(sK1),
inference(extension,[status(thm),parent(t19:2)],[f_4_7]) ).
cnf(t22,plain,
$false,
inference(connection,[status(thm),parent(t21:1)],[t21:1,t19:2]) ).
cnf(t23,plain,
( ~ sP0
| decreases(resources(sK1,sK2)) ),
inference(extension,[status(thm),parent(t19:3)],[f_4_10]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t19:3]) ).
cnf(t25,plain,
sP0,
inference(lemma_extension,[status(thm),parent(t23:2)],[l1:1]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t23:2]) ).
cnf(t27,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(extension,[status(thm),parent(t19:4)],[f_3_2]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t19:4]) ).
cnf(t29,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(extension,[status(thm),parent(t19:5)],[f_4_8]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t19:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 19 16:12:57 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.14/5.42 % SZS status Theorem for theBenchmark
% 0.14/5.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------