%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI674_1 : TPTP v9.0.0. Released v6.3.0.
% 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 : n006.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 : Wed Apr 9 05:40:49 PM UTC 2025
% Result : Theorem 3.93s 2.00s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 18 ~; 8 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 112 ( 14 atm; 46 fun; 36 num; 16 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_93,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_101,axiom,
! [A: $int,B: $int] : ( $uminus($product(A,B)) = $product($uminus(A),B) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',minus_mult_left) ).
tff(f_30,axiom,
$lesseq(4,$product(a,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f_109,axiom,
! [C: $int,B: $int] :
( ( $product(C,B) = C )
<=> ( ( C = 0 )
| ( B = 1 ) ) ),
file('/export/starexec/sandbox/solver/bin/lemmas/mult_lemmas.p',mult_cancel_right1) ).
tff(f_34,negated_conjecture,
~ ( $lesseq(a,$uminus(2))
| $lesseq(2,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(c_46,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_41,plain,
! [A_17: $int,B_18: $int,X_33: $int] :
( ( $uminus($product(A_17,B_18)) = $product(X_33,B_18) )
| ( X_33 != $uminus(A_17) ) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_43,plain,
! [X_33: $int,B_18: $int,A_17: $int] :
( ( $uminus($product(X_33,B_18)) = $product(A_17,B_18) )
| ( X_33 != $uminus(A_17) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_41]) ).
tff(c_2,plain,
$lesseq(4,$product(a,a)),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_36,plain,
~ $less($product(a,a),4),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_64,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_36]) ).
tff(c_128,plain,
$uminus($product($uminus(a),a)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_43,c_64]) ).
tff(c_199,plain,
$uminus($product(a,$uminus(a))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_46,c_128]) ).
tff(c_217,plain,
$product(a,$uminus(a)) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_199]) ).
tff(c_39,plain,
! [C_23: $int] : ( $product(C_23,1) = C_23 ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_339,plain,
( ( a = $uminus('#skE_1') )
| ( $uminus(a) != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_217,c_39]) ).
tff(c_341,plain,
( ( a = $uminus('#skE_1') )
| ( a != $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_339]) ).
tff(c_739,plain,
a != $uminus(1),
inference(splitLeft,[status(thm)],[c_341]) ).
tff(c_38,plain,
! [B_24: $int] : ( $product(0,B_24) = 0 ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_179,plain,
( ( '#skE_1' = 0 )
| ( a != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_38]) ).
tff(c_210,plain,
a != 0,
inference(splitLeft,[status(thm)],[c_179]) ).
tff(c_177,plain,
( ( a = '#skE_1' )
| ( a != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_64,c_39]) ).
tff(c_208,plain,
a != 1,
inference(splitLeft,[status(thm)],[c_177]) ).
tff(c_6,plain,
~ $lesseq(a,$uminus(2)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_31,plain,
$less($uminus(2),a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).
tff(c_4,plain,
~ $lesseq(2,a),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_32,plain,
$less(a,2),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_740,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_739,c_210,c_208,c_31,c_32]) ).
tff(c_744,plain,
a = $uminus(1),
inference(splitRight,[status(thm)],[c_341]) ).
tff(c_743,plain,
a = $uminus('#skE_1'),
inference(splitRight,[status(thm)],[c_341]) ).
tff(c_1002,plain,
$uminus('#skE_1') = $uminus(1),
inference(demodulation,[status(thm),theory(equality)],[c_744,c_743]) ).
tff(c_1005,plain,
'#skE_1' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1002]) ).
tff(c_54,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_36]) ).
tff(c_49,plain,
~ $less($product(a,a),4),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_61,plain,
~ $less('#skE_1',4),
inference(demodulation,[status(thm),theory(equality)],[c_54,c_49]) ).
tff(c_1006,plain,
~ $less(1,4),
inference(demodulation,[status(thm),theory(equality)],[c_1005,c_61]) ).
tff(c_1009,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1006]) ).
tff(c_1012,plain,
'#skE_1' = 0,
inference(splitRight,[status(thm)],[c_179]) ).
tff(c_1019,plain,
~ $less(0,4),
inference(demodulation,[status(thm),theory(equality)],[c_1012,c_61]) ).
tff(c_1025,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1019]) ).
tff(c_1029,plain,
a = 1,
inference(splitRight,[status(thm)],[c_177]) ).
tff(c_1028,plain,
a = '#skE_1',
inference(splitRight,[status(thm)],[c_177]) ).
tff(c_1045,plain,
'#skE_1' = 1,
inference(demodulation,[status(thm),theory(equality)],[c_1029,c_1028]) ).
tff(c_1046,plain,
~ $less(1,4),
inference(demodulation,[status(thm),theory(equality)],[c_1045,c_61]) ).
tff(c_1049,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI674_1 : TPTP v9.0.0. Released v6.3.0.
% 0.07/0.13 % 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
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 7 15:16:08 EDT 2025
% 0.14/0.35 % CPUTime :
% 3.93/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.93/2.01
% 3.93/2.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------