%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n012.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 : Tue Sep 8 06:02:57 AM UTC 2026
% Result : Unsatisfiable 1.50s 1.16s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subpopulations > outcompetes > greater_or_equal > greater > environment > growth_rate > #nlpp > zero > sk2 > sk1 > first_movers > efficient_producers
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(subpopulations,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(greater,type,
greater: ( $i * $i ) > $o ).
tff(sk2,type,
sk2: $i ).
tff(sk1,type,
sk1: $i ).
tff(efficient_producers,type,
efficient_producers: $i ).
tff(growth_rate,type,
growth_rate: ( $i * $i ) > $i ).
tff(environment,type,
environment: $i > $o ).
tff(first_movers,type,
first_movers: $i ).
tff(greater_or_equal,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(outcompetes,type,
outcompetes: ( $i * $i * $i ) > $o ).
tff(zero,type,
zero: $i ).
tff(f_67,axiom,
environment(sk1),
file(unknown,unknown) ).
tff(f_68,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file(unknown,unknown) ).
tff(f_30,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| subpopulations(C,B,A,D) ),
file(unknown,unknown) ).
tff(f_79,axiom,
! [A,B] :
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ outcompetes(first_movers,efficient_producers,B) ),
file(unknown,unknown) ).
tff(f_69,axiom,
greater_or_equal(growth_rate(first_movers,sk2),zero),
file(unknown,unknown) ).
tff(f_70,axiom,
greater(zero,growth_rate(efficient_producers,sk2)),
file(unknown,unknown) ).
tff(f_44,axiom,
! [A,B,C,D] :
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D))
| outcompetes(C,B,D) ),
file(unknown,unknown) ).
tff(c_10,plain,
environment(sk1),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_12,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnfTransformation,[status(thm)],[f_68]) ).
tff(c_26,plain,
! [C_21,B_22,A_23,D_24] :
( subpopulations(C_21,B_22,A_23,D_24)
| ~ subpopulations(B_22,C_21,A_23,D_24)
| ~ environment(A_23) ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_28,plain,
( subpopulations(efficient_producers,first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_12,c_26]) ).
tff(c_31,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_28]) ).
tff(c_19,plain,
! [B_19,A_20] :
( ~ outcompetes(first_movers,efficient_producers,B_19)
| ~ subpopulations(first_movers,efficient_producers,A_20,B_19)
| ~ environment(A_20) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_22,plain,
( ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1) ),
inference(resolution,[status(thm)],[c_12,c_19]) ).
tff(c_25,plain,
~ outcompetes(first_movers,efficient_producers,sk2),
inference(demodulation,[status(thm),theory(equality)],[c_10,c_22]) ).
tff(c_14,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(cnfTransformation,[status(thm)],[f_69]) ).
tff(c_16,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_60,plain,
! [C_33,B_34,D_35,A_36] :
( outcompetes(C_33,B_34,D_35)
| ~ greater(zero,growth_rate(B_34,D_35))
| ~ greater_or_equal(growth_rate(C_33,D_35),zero)
| ~ subpopulations(B_34,C_33,A_36,D_35)
| ~ environment(A_36) ),
inference(cnfTransformation,[status(thm)],[f_44]) ).
tff(c_64,plain,
! [C_37,A_38] :
( outcompetes(C_37,efficient_producers,sk2)
| ~ greater_or_equal(growth_rate(C_37,sk2),zero)
| ~ subpopulations(efficient_producers,C_37,A_38,sk2)
| ~ environment(A_38) ),
inference(resolution,[status(thm)],[c_16,c_60]) ).
tff(c_66,plain,
! [A_38] :
( outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(efficient_producers,first_movers,A_38,sk2)
| ~ environment(A_38) ),
inference(resolution,[status(thm)],[c_14,c_64]) ).
tff(c_70,plain,
! [A_39] :
( ~ subpopulations(efficient_producers,first_movers,A_39,sk2)
| ~ environment(A_39) ),
inference(negUnitSimplification,[status(thm)],[c_25,c_66]) ).
tff(c_73,plain,
~ environment(sk1),
inference(resolution,[status(thm)],[c_31,c_70]) ).
tff(c_77,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Mon Sep 7 12:42:41 UTC 2026
% 0.02/0.30 % CPUTime :
% 1.50/1.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.50/1.16
% 1.50/1.16 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------