%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI652_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 : n029.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 05:40:46 PM UTC 2025
% Result : Theorem 3.58s 1.97s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 5 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number arithmetic : 95 ( 6 atm; 51 fun; 23 num; 15 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 : 11 ( 2 usr; 7 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp
%Foreground sorts:
%Background operators:
tff('#skE_1',type,
'#skE_1': $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f_33,negated_conjecture,
$product(a,a) != 1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_002) ).
tff(f_66,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_74,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_82,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_30,axiom,
$less(2,$sum(a,4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f_31,axiom,
$lesseq($uminus(2),$difference($uminus(3),a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_001) ).
tff(c_33,plain,
$product(a,a) != 1,
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_53,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_48,plain,
$product(a,a) != 1,
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_60,plain,
'#skE_1' != 1,
inference(demodulation,[status(thm),theory(equality)],[c_53,c_48]) ).
tff(c_45,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_63,plain,
$product(a,a) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_33]) ).
tff(c_40,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_74]) ).
tff(c_42,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_40]) ).
tff(c_95,plain,
$uminus($product($uminus(a),a)) = '#skE_1',
inference(superposition,[status(thm),theory(equality)],[c_63,c_42]) ).
tff(c_169,plain,
$uminus($product(a,$uminus(a))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_45,c_95]) ).
tff(c_217,plain,
$product(a,$uminus(a)) = $uminus('#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_169]) ).
tff(c_38,plain,
! [C_23: $int] : ( $product(C_23,1) = C_23 ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_339,plain,
( ( a = $uminus('#skE_1') )
| ( $uminus(a) != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_217,c_38]) ).
tff(c_341,plain,
( ( a = $uminus('#skE_1') )
| ( a != $uminus(1) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_339]) ).
tff(c_564,plain,
a != $uminus(1),
inference(splitLeft,[status(thm)],[c_341]) ).
tff(c_1,plain,
$less(2,$sum(a,4)),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_35,plain,
$less($uminus(2),a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_3,plain,
$lesseq($uminus(2),$difference($uminus(3),a)),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_34,plain,
~ $less($uminus(1),a),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_565,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_564,c_35,c_34]) ).
tff(c_569,plain,
a = $uminus(1),
inference(splitRight,[status(thm)],[c_341]) ).
tff(c_568,plain,
a = $uminus('#skE_1'),
inference(splitRight,[status(thm)],[c_341]) ).
tff(c_615,plain,
$uminus('#skE_1') = $uminus(1),
inference(demodulation,[status(thm),theory(equality)],[c_569,c_568]) ).
tff(c_617,plain,
'#skE_1' = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615]) ).
tff(c_619,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_60,c_617]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI652_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
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 15:15:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 3.58/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.58/1.97
% 3.58/1.97 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------