%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX153_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/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 : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:56:31 PM UTC 2026
% Result : Theorem 2.72s 1.63s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 30 ( 12 ~; 11 |; 2 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 68 ( 10 atm; 6 fun; 21 num; 31 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 29 !; 2 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
%$ w1w2 > w1sl2 > w1cr2 > sl1w2 > sl1sl2 > sl1cr2 > cr1w2 > cr1sl2 > cr1cr2 > #nlpp
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(w1w2,type,
w1w2: ( $int * $int ) > $o ).
tff(sl1w2,type,
sl1w2: ( $int * $int ) > $o ).
tff(cr1w2,type,
cr1w2: ( $int * $int ) > $o ).
tff(sl1cr2,type,
sl1cr2: ( $int * $int ) > $o ).
tff(cr1cr2,type,
cr1cr2: ( $int * $int ) > $o ).
tff(w1cr2,type,
w1cr2: ( $int * $int ) > $o ).
tff(w1sl2,type,
w1sl2: ( $int * $int ) > $o ).
tff(sl1sl2,type,
sl1sl2: ( $int * $int ) > $o ).
tff(cr1sl2,type,
cr1sl2: ( $int * $int ) > $o ).
tff(f_134,negated_conjecture,
~ ( ! [Xa: $int,Ya: $int] :
( ( $greatereq(Xa,0)
& $greatereq(Ya,0) )
=> sl1sl2(Xa,Ya) )
=> ? [Ua: $int,Va: $int] : cr1w2(Ua,Va) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj1) ).
tff(f_80,axiom,
! [Xa: $int,Ya: $int] :
( sl1sl2(Xa,Ya)
=> w1sl2($sum(Ya,1),Ya) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
tff(f_104,axiom,
! [Xa: $int,Ya: $int] :
( cr1sl2(Xa,Ya)
=> cr1w2(Xa,$sum(Xa,1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
tff(f_88,axiom,
! [Xa: $int,Ya: $int] :
( ( w1sl2(Xa,Ya)
& ( ( Ya = 0 )
| $less(Xa,Ya) ) )
=> cr1sl2(Xa,Ya) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
tff(c_51,plain,
! [X_37a: $int,Y_38a: $int] :
( sl1sl2(X_37a,Y_38a)
| ~ $greatereq(X_37a,0)
| ~ $greatereq(Y_38a,0) ),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_53,plain,
! [X_37a: $int,Y_38a: $int] :
( sl1sl2(X_37a,Y_38a)
| $less(X_37a,0)
| $less(Y_38a,0) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_51]) ).
tff(c_26,plain,
! [Y_20a: $int,X_19a: $int] :
( w1sl2($sum(Y_20a,1),Y_20a)
| ~ sl1sl2(X_19a,Y_20a) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_151,plain,
! [Y_78a: $int,X_79a: $int] :
( w1sl2($sum(1,Y_78a),Y_78a)
| ~ sl1sl2(X_79a,Y_78a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_26]) ).
tff(c_54,plain,
! [U_39a: $int,V_40a: $int] : ~ cr1w2(U_39a,V_40a),
inference(cnfTransformation,[status(thm)],[f_134]) ).
tff(c_38,plain,
! [X_27a: $int,Y_28a: $int] :
( cr1w2(X_27a,$sum(X_27a,1))
| ~ cr1sl2(X_27a,Y_28a) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_63,plain,
! [X_27a: $int,Y_28a: $int] :
( cr1w2(X_27a,$sum(1,X_27a))
| ~ cr1sl2(X_27a,Y_28a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_38]) ).
tff(c_106,plain,
! [X_27a: $int,Y_28a: $int] : ~ cr1sl2(X_27a,Y_28a),
inference(negUnitSimplification,[status(thm)],[c_54,c_63]) ).
tff(c_70,plain,
! [X_21a: $int] :
( cr1sl2(X_21a,0)
| ~ w1sl2(X_21a,0) ),
inference(cnfTransformation,[status(thm)],[f_88]) ).
tff(c_115,plain,
! [X_21a: $int] : ~ w1sl2(X_21a,0),
inference(negUnitSimplification,[status(thm)],[c_106,c_70]) ).
tff(c_177,plain,
! [X_83a: $int] : ~ sl1sl2(X_83a,0),
inference(resolution,[status(thm)],[c_151,c_115]) ).
tff(c_182,plain,
! [X_37a: $int] :
( $less(X_37a,0)
| $less(0,0) ),
inference(resolution,[status(thm)],[c_53,c_177]) ).
tff(c_184,plain,
! [X_37a: $int] : $less(X_37a,0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_182]) ).
tff(c_196,plain,
$false,
inference(quantifierElimination,[status(thm),theory('LIA')],[c_184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.07 % 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
% 0.08/0.25 % Computer : n012.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue May 5 08:56:45 EDT 2026
% 0.08/0.26 % CPUTime :
% 2.72/1.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.72/1.64
% 2.72/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------