%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ALG070+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 : n013.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 05:24:06 PM UTC 2025
% Result : Theorem 4.10s 2.66s
% Output : CNFRefutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 93 ( 24 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 99 ( 43 ~; 35 |; 4 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 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 : 31 ( 31 !; 0 ?; 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_60,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> ( ( op2(U,U) != V )
| ( op2(U,V) = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f_39,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
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_32,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f_49,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> ( ( op1(U,U) != V )
| ( op1(U,V) = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(c_8,plain,
op2('#skF_1','#skF_2') != '#skF_1',
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_14,plain,
sorti2('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_12,plain,
sorti2('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_4,plain,
! [U_4,V_6] :
( sorti2(op2(U_4,V_6))
| ~ sorti2(V_6)
| ~ sorti2(U_4) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_24,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_10,plain,
op2('#skF_1','#skF_1') = '#skF_2',
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_107,plain,
! [Y_33,Z_34] :
( ( op1(j(Y_33),j(Z_34)) = j(op2(Y_33,Z_34)) )
| ~ sorti2(Z_34)
| ~ sorti2(Y_33) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
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_136,plain,
! [Y_37,Z_38] :
( sorti1(j(op2(Y_37,Z_38)))
| ~ sorti1(j(Z_38))
| ~ sorti1(j(Y_37))
| ~ sorti2(Z_38)
| ~ sorti2(Y_37) ),
inference(superposition,[status(thm),theory(equality)],[c_107,c_2]) ).
tff(c_142,plain,
( sorti1(j('#skF_2'))
| ~ sorti1(j('#skF_1'))
| ~ sorti1(j('#skF_1'))
| ~ sorti2('#skF_1')
| ~ sorti2('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_136]) ).
tff(c_144,plain,
( sorti1(j('#skF_2'))
| ~ sorti1(j('#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14,c_142]) ).
tff(c_145,plain,
~ sorti1(j('#skF_1')),
inference(splitLeft,[status(thm)],[c_144]) ).
tff(c_148,plain,
~ sorti2('#skF_1'),
inference(resolution,[status(thm)],[c_24,c_145]) ).
tff(c_152,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_148]) ).
tff(c_154,plain,
sorti1(j('#skF_1')),
inference(splitRight,[status(thm)],[c_144]) ).
tff(c_90,plain,
! [U_31] :
( ( op1(U_31,op1(U_31,U_31)) = U_31 )
| ~ sorti1(op1(U_31,U_31))
| ~ sorti1(U_31) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_94,plain,
! [V_3] :
( ( op1(V_3,op1(V_3,V_3)) = V_3 )
| ~ sorti1(V_3) ),
inference(resolution,[status(thm)],[c_2,c_90]) ).
tff(c_319,plain,
! [Z_47] :
( ( op1(j(Z_47),j(op2(Z_47,Z_47))) = j(Z_47) )
| ~ sorti1(j(Z_47))
| ~ sorti2(Z_47)
| ~ sorti2(Z_47) ),
inference(superposition,[status(thm),theory(equality)],[c_107,c_94]) ).
tff(c_368,plain,
( ( op1(j('#skF_1'),j('#skF_2')) = j('#skF_1') )
| ~ sorti1(j('#skF_1'))
| ~ sorti2('#skF_1')
| ~ sorti2('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_319]) ).
tff(c_372,plain,
op1(j('#skF_1'),j('#skF_2')) = j('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14,c_154,c_368]) ).
tff(c_20,plain,
! [Y_16,Z_18] :
( ( op1(j(Y_16),j(Z_18)) = j(op2(Y_16,Z_18)) )
| ~ sorti2(Z_18)
| ~ sorti2(Y_16) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_403,plain,
( ( j(op2('#skF_1','#skF_2')) = j('#skF_1') )
| ~ sorti2('#skF_2')
| ~ sorti2('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_372,c_20]) ).
tff(c_419,plain,
j(op2('#skF_1','#skF_2')) = j('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_12,c_403]) ).
tff(c_18,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_446,plain,
( ( h(j('#skF_1')) = op2('#skF_1','#skF_2') )
| ~ sorti2(op2('#skF_1','#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_419,c_18]) ).
tff(c_463,plain,
~ sorti2(op2('#skF_1','#skF_2')),
inference(splitLeft,[status(thm)],[c_446]) ).
tff(c_466,plain,
( ~ sorti2('#skF_2')
| ~ sorti2('#skF_1') ),
inference(resolution,[status(thm)],[c_4,c_463]) ).
tff(c_470,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_12,c_466]) ).
tff(c_471,plain,
h(j('#skF_1')) = op2('#skF_1','#skF_2'),
inference(splitRight,[status(thm)],[c_446]) ).
tff(c_491,plain,
( ( op2('#skF_1','#skF_2') = '#skF_1' )
| ~ sorti2('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_471,c_18]) ).
tff(c_514,plain,
op2('#skF_1','#skF_2') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_14,c_491]) ).
tff(c_516,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG070+1 : TPTP v9.0.0. Released v2.7.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Apr 6 06:59:02 EDT 2025
% 0.14/0.35 % CPUTime :
% 4.10/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.10/2.66
% 4.10/2.66 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------