%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : PLA060_1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n025.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 06:48:45 PM UTC 2026
% Result : Theorem 3.03s 1.76s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 73 ( 1 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 68 ( 17 ~; 41 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 140 ( 39 atm; 10 fun; 39 num; 52 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 0 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 50 !; 2 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
%$ s4 > s3 > s2 > s1 > s0 > #nlpp
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(s3,type,
s3: ( $int * $int ) > $o ).
tff(s1,type,
s1: ( $int * $int ) > $o ).
tff(s0,type,
s0: ( $int * $int ) > $o ).
tff(s2,type,
s2: ( $int * $int ) > $o ).
tff(s4,type,
s4: ( $int * $int ) > $o ).
tff(f_77,negated_conjecture,
~ ( ! [Xa: $int,Ya: $int] :
( $lesseq(Xa,200)
=> s0(Xa,Ya) )
=> ? [Ua: $int,Va: $int] :
( s0(Ua,Va)
& $greatereq(Ua,240) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj1) ).
tff(f_39,axiom,
! [Xa: $int,Ya: $int] :
( ( s0(Xa,Ya)
& $lesseq(Xa,200) )
=> s3(Xa,Ya) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
tff(f_55,axiom,
! [Xa: $int,Ya: $int,Za: $int] :
( ( s3(Xa,Ya)
& $lesseq(Za,40)
& $greatereq(Za,0) )
=> s4(Xa,Za) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f_67,axiom,
! [Xa: $int,Ya: $int,Za: $int] :
( ( s4(Xa,Ya)
& ( Za = $sum(Xa,Ya) ) )
=> s0(Za,Ya) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
tff(c_16,plain,
! [X_17a: $int,Y_18a: $int] :
( s0(X_17a,Y_18a)
| ~ $lesseq(X_17a,200) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_18,plain,
! [X_17a: $int,Y_18a: $int] :
( s0(X_17a,Y_18a)
| $less(200,X_17a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_16]) ).
tff(c_3,plain,
! [X_3a: $int,Y_4a: $int] :
( s3(X_3a,Y_4a)
| ~ s0(X_3a,Y_4a)
| ~ $lesseq(X_3a,200) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_31,plain,
! [X_3a: $int,Y_4a: $int] :
( s3(X_3a,Y_4a)
| ~ s0(X_3a,Y_4a)
| $less(200,X_3a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_7,plain,
! [X_8a: $int,Z_10a: $int,Y_9a: $int] :
( s4(X_8a,Z_10a)
| ~ s3(X_8a,Y_9a)
| ~ $lesseq(Z_10a,40)
| ~ $greatereq(Z_10a,0) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_45,plain,
! [X_32a: $int,Z_33a: $int,Y_34a: $int] :
( s4(X_32a,Z_33a)
| ~ s3(X_32a,Y_34a)
| $less(40,Z_33a)
| $less(Z_33a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_23,plain,
! [X_14a: $int,Y_15a: $int] :
( s0($sum(X_14a,Y_15a),Y_15a)
| ~ s4(X_14a,Y_15a) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_49,plain,
! [X_32a: $int,Z_33a: $int,Y_34a: $int] :
( s0($sum(X_32a,Z_33a),Z_33a)
| ~ s3(X_32a,Y_34a)
| $less(40,Z_33a)
| $less(Z_33a,0) ),
inference(resolution,[status(thm)],[c_45,c_23]) ).
tff(c_66,plain,
! [Z_48a: $int,X_49a: $int,Y_50a: $int] :
( s0($sum(Z_48a,X_49a),Z_48a)
| ~ s3(X_49a,Y_50a)
| $less(40,Z_48a)
| $less(Z_48a,0) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_49]) ).
tff(c_70,plain,
! [Z_48a: $int,X_3a: $int,Y_4a: $int] :
( s0($sum(Z_48a,X_3a),Z_48a)
| $less(40,Z_48a)
| $less(Z_48a,0)
| ~ s0(X_3a,Y_4a)
| $less(200,X_3a) ),
inference(resolution,[status(thm)],[c_31,c_66]) ).
tff(c_85,plain,
! [X_59a: $int,Z_58a: $int,Y_60a: $int] :
( s0($sum(X_59a,Z_58a),Z_58a)
| $less(40,Z_58a)
| $less(Z_58a,0)
| ~ s0(X_59a,Y_60a)
| $less(200,X_59a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_70]) ).
tff(c_88,plain,
! [X_17a: $int,Z_58a: $int] :
( s0($sum(X_17a,Z_58a),Z_58a)
| $less(40,Z_58a)
| $less(Z_58a,0)
| $less(200,X_17a) ),
inference(resolution,[status(thm)],[c_18,c_85]) ).
tff(c_94,plain,
! [Z_63a: $int,X_64a: $int] :
( s0($sum(Z_63a,X_64a),Z_63a)
| $less(40,Z_63a)
| $less(Z_63a,0)
| $less(200,X_64a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_88]) ).
tff(c_14,plain,
! [U_19a: $int,V_20a: $int] :
( ~ s0(U_19a,V_20a)
| ~ $greatereq(U_19a,240) ),
inference(cnfTransformation,[status(thm)],[f_77]) ).
tff(c_19,plain,
! [U_19a: $int,V_20a: $int] :
( ~ s0(U_19a,V_20a)
| $less(U_19a,240) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_14]) ).
tff(c_104,plain,
! [Z_63a: $int,X_64a: $int] :
( $less($sum(Z_63a,X_64a),240)
| $less(40,Z_63a)
| $less(Z_63a,0)
| $less(200,X_64a) ),
inference(resolution,[status(thm)],[c_94,c_19]) ).
tff(c_106,plain,
! [X_64a: $int,Z_63a: $int] :
( $less($sum(X_64a,Z_63a),240)
| $less(40,Z_63a)
| $less(Z_63a,0)
| $less(200,X_64a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_104]) ).
tff(c_108,plain,
$false,
inference(quantifierElimination,[status(thm),theory('LIA')],[c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PLA060_1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:52:28 EDT 2026
% 0.16/0.34 % CPUTime :
% 3.03/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.03/1.76
% 3.03/1.76 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------