%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG203+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 : n007.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 05:24:45 PM UTC 2025
% Result : Theorem 5.11s 2.25s
% Output : CNFRefutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 24 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 86 ( 38 ~; 27 |; 10 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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; 2 con; 0-2 aty)
% Number of variables : 30 ( 26 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sorti2 > sorti1 > op2 > op1 > #nlpp > j > h > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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('#skF_1',type,
'#skF_1': $i ).
tff(sorti1,type,
sorti1: $i > $o ).
tff(h,type,
h: $i > $i ).
tff(j,type,
j: $i > $i ).
tff(f_49,axiom,
( ? [U] :
( sorti1(U)
& ( op1(U,U) = U ) )
& ? [V] :
( sorti1(V)
& ( op1(V,V) != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f_32,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f_97,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_60,axiom,
~ ( ? [U] :
( sorti2(U)
& ( op2(U,U) = U ) )
& ? [V] :
( sorti2(V)
& ( op2(V,V) != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(c_6,plain,
op1('#skF_1','#skF_1') != '#skF_1',
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_8,plain,
sorti1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_2,plain,
! [U_1,V_3] :
( sorti1(op1(U_1,V_3))
| ~ sorti1(V_3)
| ~ sorti1(U_1) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_22,plain,
! [W_11,X_13] :
( ( op2(h(W_11),h(X_13)) = h(op1(W_11,X_13)) )
| ~ sorti1(X_13)
| ~ sorti1(W_11) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_26,plain,
! [U_9] :
( sorti2(h(U_9))
| ~ sorti1(U_9) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_12,plain,
sorti1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_10,plain,
op1('#skF_2','#skF_2') = '#skF_2',
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_14,plain,
! [V_8,U_7] :
( ( op2(V_8,V_8) = V_8 )
| ~ sorti2(V_8)
| ( op2(U_7,U_7) != U_7 )
| ~ sorti2(U_7) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_91,plain,
! [U_29] :
( ( op2(U_29,U_29) != U_29 )
| ~ sorti2(U_29) ),
inference(splitLeft,[status(thm)],[c_14]) ).
tff(c_113,plain,
! [X_32] :
( ( h(op1(X_32,X_32)) != h(X_32) )
| ~ sorti2(h(X_32))
| ~ sorti1(X_32)
| ~ sorti1(X_32) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_91]) ).
tff(c_118,plain,
( ~ sorti2(h('#skF_2'))
| ~ sorti1('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_113]) ).
tff(c_121,plain,
~ sorti2(h('#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_118]) ).
tff(c_133,plain,
~ sorti1('#skF_2'),
inference(resolution,[status(thm)],[c_26,c_121]) ).
tff(c_137,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_133]) ).
tff(c_139,plain,
! [V_35] :
( ( op2(V_35,V_35) = V_35 )
| ~ sorti2(V_35) ),
inference(splitRight,[status(thm)],[c_14]) ).
tff(c_146,plain,
! [U_36] :
( ( op2(h(U_36),h(U_36)) = h(U_36) )
| ~ sorti1(U_36) ),
inference(resolution,[status(thm)],[c_26,c_139]) ).
tff(c_189,plain,
! [X_39] :
( ( h(op1(X_39,X_39)) = h(X_39) )
| ~ sorti1(X_39)
| ~ sorti1(X_39)
| ~ sorti1(X_39) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_146]) ).
tff(c_16,plain,
! [X2_18] :
( ( j(h(X2_18)) = X2_18 )
| ~ sorti1(X2_18) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_1811,plain,
! [X_77] :
( ( op1(X_77,X_77) = j(h(X_77)) )
| ~ sorti1(op1(X_77,X_77))
| ~ sorti1(X_77)
| ~ sorti1(X_77)
| ~ sorti1(X_77) ),
inference(superposition,[status(thm),theory(equality)],[c_189,c_16]) ).
tff(c_1930,plain,
! [V_78] :
( ( op1(V_78,V_78) = j(h(V_78)) )
| ~ sorti1(V_78) ),
inference(resolution,[status(thm)],[c_2,c_1811]) ).
tff(c_2057,plain,
! [V_79] :
( ( op1(V_79,V_79) = V_79 )
| ~ sorti1(V_79)
| ~ sorti1(V_79) ),
inference(superposition,[status(thm),theory(equality)],[c_1930,c_16]) ).
tff(c_2065,plain,
( ( op1('#skF_1','#skF_1') = '#skF_1' )
| ~ sorti1('#skF_1') ),
inference(resolution,[status(thm)],[c_8,c_2057]) ).
tff(c_2073,plain,
op1('#skF_1','#skF_1') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_8,c_2065]) ).
tff(c_2075,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_2073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG203+1 : TPTP v9.0.0. Released v2.7.0.
% 0.08/0.13 % 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
% 0.13/0.34 % Computer : n007.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 : Sun Apr 6 07:09:37 EDT 2025
% 0.13/0.34 % CPUTime :
% 5.11/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.11/2.25
% 5.11/2.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------