%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG069+1 : TPTP v9.0.0. Released v2.7.0.
% 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 : n032.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 05:24:05 PM UTC 2025
% Result : Theorem 3.58s 2.33s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 15 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 65 ( 29 ~; 19 |; 6 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 23 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sorti2 > sorti1 > op2 > op1 > #nlpp > j > h > #skF_1 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(op2,type,
op2: ( $i * $i ) > $i ).
tff(op1,type,
op1: ( $i * $i ) > $i ).
tff(sorti2,type,
sorti2: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i ).
tff(sorti1,type,
sorti1: $i > $o ).
tff(h,type,
h: $i > $i ).
tff(j,type,
j: $i > $i ).
tff(f_91,negated_conjecture,
~ ( ( ! [U] :
( sorti1(U)
=> sorti2(h(U)) )
& ! [V] :
( sorti2(V)
=> sorti1(j(V)) ) )
=> ~ ( ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> ( h(op1(W,X)) = op2(h(W),h(X)) ) ) )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> ( j(op2(Y,Z)) = op1(j(Y),j(Z)) ) ) )
& ! [X1] :
( sorti2(X1)
=> ( h(j(X1)) = X1 ) )
& ! [X2] :
( sorti1(X2)
=> ( j(h(X2)) = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_46,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( sorti1(V)
& ( op1(V,V) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f_54,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( sorti2(V)
& ( op2(V,V) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(c_16,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_22,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_8,plain,
! [U_7] :
( sorti1('#skF_1'(U_7))
| ~ sorti1(U_7) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_24,plain,
! [U_11] :
( sorti2(h(U_11))
| ~ sorti1(U_11) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_6,plain,
! [U_7] :
( ( op1('#skF_1'(U_7),'#skF_1'(U_7)) = U_7 )
| ~ sorti1(U_7) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_93,plain,
! [W_34,X_35] :
( ( op2(h(W_34),h(X_35)) = h(op1(W_34,X_35)) )
| ~ sorti1(X_35)
| ~ sorti1(W_34) ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_10,plain,
! [V_10] :
( ( op2(V_10,V_10) != '#skF_2' )
| ~ sorti2(V_10) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_114,plain,
! [X_36] :
( ( h(op1(X_36,X_36)) != '#skF_2' )
| ~ sorti2(h(X_36))
| ~ sorti1(X_36)
| ~ sorti1(X_36) ),
inference(superposition,[status(thm),theory(equality)],[c_93,c_10]) ).
tff(c_161,plain,
! [U_43] :
( ( h(U_43) != '#skF_2' )
| ~ sorti2(h('#skF_1'(U_43)))
| ~ sorti1('#skF_1'(U_43))
| ~ sorti1('#skF_1'(U_43))
| ~ sorti1(U_43) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_114]) ).
tff(c_166,plain,
! [U_44] :
( ( h(U_44) != '#skF_2' )
| ~ sorti1(U_44)
| ~ sorti1('#skF_1'(U_44)) ),
inference(resolution,[status(thm)],[c_24,c_161]) ).
tff(c_171,plain,
! [U_45] :
( ( h(U_45) != '#skF_2' )
| ~ sorti1(U_45) ),
inference(resolution,[status(thm)],[c_8,c_166]) ).
tff(c_188,plain,
! [V_46] :
( ( h(j(V_46)) != '#skF_2' )
| ~ sorti2(V_46) ),
inference(resolution,[status(thm)],[c_22,c_171]) ).
tff(c_199,plain,
~ sorti2('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_16,c_188]) ).
tff(c_12,plain,
sorti2('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_201,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_199,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG069+1 : TPTP v9.0.0. Released v2.7.0.
% 0.00/0.10 % 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
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun Apr 6 06:59:01 EDT 2025
% 0.09/0.30 % CPUTime :
% 3.58/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.58/2.33
% 3.58/2.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------