%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 : Fri Sep 25 02:11:19 PM UTC 2026
% Result : Unsatisfiable 3.77s 1.05s
% Output : Proof 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 18 unt; 0 def)
% Number of atoms : 199 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 236 ( 110 ~; 126 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( in_environment(A,B)
| ~ in_environment(A,C)
| ~ greater(C,B)
| ~ greater_or_equal(B,start_time(A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order_28) ).
fof(f6_nnf,plain,
! [A,B,C] :
( in_environment(A,B)
| ~ in_environment(A,C)
| ~ greater(C,B)
| ~ greater_or_equal(B,start_time(A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( in_environment(A,B)
| ~ in_environment(A,C)
| ~ greater(C,B)
| ~ greater_or_equal(B,start_time(A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f11,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2_33) ).
fof(f11_nnf,plain,
environment(sk1),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p35,plain,
( in_environment(sk1,X0)
| ~ in_environment(sk1,X1)
| ~ greater(X1,X0)
| ~ greater_or_equal(X0,start_time(sk1)) ),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(f5,axiom,
( greater_or_equal(initial_FM_EP(A),start_time(A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time_27) ).
fof(f5_nnf,plain,
! [A] :
( greater_or_equal(initial_FM_EP(A),start_time(A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] :
( greater_or_equal(initial_FM_EP(A),start_time(A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p14,plain,
greater_or_equal(initial_FM_EP(sk1),start_time(sk1)),
inference(resolution,[status(thm)],[c5,c11]) ).
cnf(p36,plain,
( in_environment(sk1,initial_FM_EP(sk1))
| ~ in_environment(sk1,X0)
| ~ greater(X0,initial_FM_EP(sk1)) ),
inference(resolution,[status(thm)],[p35,p14]) ).
cnf(f2,axiom,
( greater_or_equal(B,initial_FM_EP(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point_24) ).
fof(f2_nnf,plain,
! [A,B] :
( greater_or_equal(B,initial_FM_EP(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( greater_or_equal(B,initial_FM_EP(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p20,plain,
( greater_or_equal(X0,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c2,c11]) ).
cnf(f12,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2_34) ).
fof(f12_nnf,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p21,plain,
greater_or_equal(sk2,initial_FM_EP(sk1)),
inference(resolution,[status(thm)],[p20,c12]) ).
cnf(f8,axiom,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_30) ).
fof(f8_nnf,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p22,plain,
( sk2 = initial_FM_EP(sk1)
| greater(sk2,initial_FM_EP(sk1)) ),
inference(resolution,[status(thm)],[p21,c8]) ).
cnf(p38,plain,
( sk2 = initial_FM_EP(sk1)
| in_environment(sk1,initial_FM_EP(sk1))
| ~ in_environment(sk1,sk2) ),
inference(resolution,[status(thm)],[p36,p22]) ).
cnf(f4,axiom,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occurs_26) ).
fof(f4_nnf,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p30,plain,
( in_environment(sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(p31,plain,
in_environment(sk1,sk2),
inference(resolution,[status(thm)],[p30,c12]) ).
cnf(p39,plain,
( sk2 = initial_FM_EP(sk1)
| in_environment(sk1,initial_FM_EP(sk1)) ),
inference(resolution,[status(thm)],[p38,p31]) ).
cnf(f1,axiom,
( subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A))
| ~ in_environment(A,initial_FM_EP(A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point_23) ).
fof(f1_nnf,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A))
| ~ in_environment(A,initial_FM_EP(A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A))
| ~ in_environment(A,initial_FM_EP(A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p17,plain,
( subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ in_environment(sk1,initial_FM_EP(sk1)) ),
inference(resolution,[status(thm)],[c1,c11]) ).
cnf(p40,plain,
( subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p39,p17]) ).
cnf(p44,plain,
( greater_or_equal(initial_FM_EP(sk1),initial_FM_EP(sk1))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p40,p20]) ).
cnf(f3,axiom,
( greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(B,C)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference_25) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(B,C)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(B,C)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X1,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p25,plain,
( greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[c3,c11]) ).
cnf(p45,plain,
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(X0,initial_FM_EP(sk1))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p44,p25]) ).
cnf(p58,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p45,p21]) ).
cnf(p59,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p58,c12]) ).
cnf(f9,hypothesis,
( greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A)))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8_31) ).
fof(f9_nnf,plain,
! [A] :
( greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A)))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A)))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p41,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(p60,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p59,p41]) ).
cnf(f0,axiom,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_22) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c0,c11]) ).
cnf(p43,plain,
( ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p40,p15]) ).
cnf(p61,plain,
( sk2 = initial_FM_EP(sk1)
| greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[status(thm)],[p60,p43]) ).
cnf(p62,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| sk2 = initial_FM_EP(sk1) ),
inference(factoring,[status(thm)],[p61]) ).
cnf(f13,negated_conjecture,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2_35) ).
fof(f13_nnf,plain,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p63,plain,
sk2 = initial_FM_EP(sk1),
inference(resolution,[status(thm)],[p62,c13]) ).
cnf(p70,plain,
greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,initial_FM_EP(sk1))),
inference(superposition,[status(thm)],[p63,p41]) ).
cnf(p77,plain,
greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(superposition,[status(thm)],[p63,p70]) ).
cnf(p89,plain,
$false,
inference(resolution,[status(thm)],[p77,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n020.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 01:02:47 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.77/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.77/1.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------