TSTP Solution File: ALG073+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG073+1 : TPTP v8.1.2. Released v2.7.0.
% 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 : n016.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 : Tue Aug 22 10:31:05 EDT 2023
% Result : Theorem 8.31s 3.07s
% Output : CNFRefutation 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 20 unt; 8 typ; 0 def)
% Number of atoms : 182 ( 58 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 227 ( 106 ~; 98 |; 12 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 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 : 52 (; 48 !; 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_51,axiom,
? [U] :
( sorti1(U)
& ? [V] :
( sorti1(V)
& ( op1(U,U) = V )
& ( op1(V,V) = U )
& ( op1(U,V) != U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f_101,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/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_39,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
tff(f_64,axiom,
~ ? [U] :
( sorti2(U)
& ? [V] :
( sorti2(V)
& ( op2(U,U) = V )
& ( op2(V,V) = U )
& ( op2(U,V) != U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
tff(c_6,plain,
op1('#skF_1','#skF_2') != '#skF_1',
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_12,plain,
sorti1('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_28,plain,
! [U_11] :
( sorti2(h(U_11))
| ~ sorti1(U_11) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_8,plain,
op1('#skF_2','#skF_2') = '#skF_1',
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_24,plain,
! [W_13,X_15] :
( ( op2(h(W_13),h(X_15)) = h(op1(W_13,X_15)) )
| ~ sorti1(X_15)
| ~ sorti1(W_13) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_86,plain,
! [U_27,V_28] :
( sorti2(op2(U_27,V_28))
| ~ sorti2(V_28)
| ~ sorti2(U_27) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_119,plain,
! [W_33,X_34] :
( sorti2(h(op1(W_33,X_34)))
| ~ sorti2(h(X_34))
| ~ sorti2(h(W_33))
| ~ sorti1(X_34)
| ~ sorti1(W_33) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_86]) ).
tff(c_125,plain,
( sorti2(h('#skF_1'))
| ~ sorti2(h('#skF_2'))
| ~ sorti2(h('#skF_2'))
| ~ sorti1('#skF_2')
| ~ sorti1('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_119]) ).
tff(c_130,plain,
( sorti2(h('#skF_1'))
| ~ sorti2(h('#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_12,c_125]) ).
tff(c_133,plain,
~ sorti2(h('#skF_2')),
inference(splitLeft,[status(thm)],[c_130]) ).
tff(c_145,plain,
~ sorti1('#skF_2'),
inference(resolution,[status(thm)],[c_28,c_133]) ).
tff(c_149,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_12,c_145]) ).
tff(c_151,plain,
sorti2(h('#skF_2')),
inference(splitRight,[status(thm)],[c_130]) ).
tff(c_18,plain,
! [X2_20] :
( ( j(h(X2_20)) = X2_20 )
| ~ sorti1(X2_20) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_101,plain,
! [Y_31,Z_32] :
( ( op1(j(Y_31),j(Z_32)) = j(op2(Y_31,Z_32)) )
| ~ sorti2(Z_32)
| ~ sorti2(Y_31) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_226,plain,
! [X2_42,Z_43] :
( ( j(op2(h(X2_42),Z_43)) = op1(X2_42,j(Z_43)) )
| ~ sorti2(Z_43)
| ~ sorti2(h(X2_42))
| ~ sorti1(X2_42) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_101]) ).
tff(c_1175,plain,
! [W_91,X_92] :
( ( op1(W_91,j(h(X_92))) = j(h(op1(W_91,X_92))) )
| ~ sorti2(h(X_92))
| ~ sorti2(h(W_91))
| ~ sorti1(W_91)
| ~ sorti1(X_92)
| ~ sorti1(W_91) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_226]) ).
tff(c_1424,plain,
! [W_97,X2_98] :
( ( j(h(op1(W_97,X2_98))) = op1(W_97,X2_98) )
| ~ sorti2(h(X2_98))
| ~ sorti2(h(W_97))
| ~ sorti1(W_97)
| ~ sorti1(X2_98)
| ~ sorti1(W_97)
| ~ sorti1(X2_98) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_1175]) ).
tff(c_1508,plain,
( ( j(h('#skF_1')) = op1('#skF_2','#skF_2') )
| ~ sorti2(h('#skF_2'))
| ~ sorti2(h('#skF_2'))
| ~ sorti1('#skF_2')
| ~ sorti1('#skF_2')
| ~ sorti1('#skF_2')
| ~ sorti1('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_1424]) ).
tff(c_1518,plain,
j(h('#skF_1')) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_12,c_12,c_12,c_12,c_151,c_151,c_8,c_1508]) ).
tff(c_150,plain,
sorti2(h('#skF_1')),
inference(splitRight,[status(thm)],[c_130]) ).
tff(c_14,plain,
sorti1('#skF_1'),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_10,plain,
op1('#skF_1','#skF_1') = '#skF_2',
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_1511,plain,
( ( j(h('#skF_2')) = op1('#skF_1','#skF_1') )
| ~ sorti2(h('#skF_1'))
| ~ sorti2(h('#skF_1'))
| ~ sorti1('#skF_1')
| ~ sorti1('#skF_1')
| ~ sorti1('#skF_1')
| ~ sorti1('#skF_1') ),
inference(superposition,[status(thm),theory(equality)],[c_10,c_1424]) ).
tff(c_1520,plain,
j(h('#skF_2')) = '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14,c_14,c_14,c_150,c_150,c_10,c_1511]) ).
tff(c_20,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_71,plain,
! [W_25,X_26] :
( ( op2(h(W_25),h(X_26)) = h(op1(W_25,X_26)) )
| ~ sorti1(X_26)
| ~ sorti1(W_25) ),
inference(cnfTransformation,[status(thm)],[f_101]) ).
tff(c_80,plain,
! [X1_19,X_26] :
( ( h(op1(j(X1_19),X_26)) = op2(X1_19,h(X_26)) )
| ~ sorti1(X_26)
| ~ sorti1(j(X1_19))
| ~ sorti2(X1_19) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_71]) ).
tff(c_1639,plain,
! [X_26] :
( ( op2(h('#skF_2'),h(X_26)) = h(op1('#skF_2',X_26)) )
| ~ sorti1(X_26)
| ~ sorti1(j(h('#skF_2')))
| ~ sorti2(h('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1520,c_80]) ).
tff(c_2967,plain,
! [X_120] :
( ( op2(h('#skF_2'),h(X_120)) = h(op1('#skF_2',X_120)) )
| ~ sorti1(X_120) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_12,c_1520,c_1639]) ).
tff(c_5340,plain,
! [X1_145] :
( ( h(op1('#skF_2',j(X1_145))) = op2(h('#skF_2'),X1_145) )
| ~ sorti1(j(X1_145))
| ~ sorti2(X1_145) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_2967]) ).
tff(c_5484,plain,
( ( op2(h('#skF_2'),h('#skF_2')) = h(op1('#skF_2','#skF_2')) )
| ~ sorti1(j(h('#skF_2')))
| ~ sorti2(h('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1520,c_5340]) ).
tff(c_5539,plain,
op2(h('#skF_2'),h('#skF_2')) = h('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_12,c_1520,c_8,c_5484]) ).
tff(c_1550,plain,
! [X_26] :
( ( op2(h('#skF_1'),h(X_26)) = h(op1('#skF_1',X_26)) )
| ~ sorti1(X_26)
| ~ sorti1(j(h('#skF_1')))
| ~ sorti2(h('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_1518,c_80]) ).
tff(c_2438,plain,
! [X_115] :
( ( op2(h('#skF_1'),h(X_115)) = h(op1('#skF_1',X_115)) )
| ~ sorti1(X_115) ),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_14,c_1518,c_1550]) ).
tff(c_6082,plain,
! [X1_150] :
( ( h(op1('#skF_1',j(X1_150))) = op2(h('#skF_1'),X1_150) )
| ~ sorti1(j(X1_150))
| ~ sorti2(X1_150) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_2438]) ).
tff(c_6238,plain,
( ( op2(h('#skF_1'),h('#skF_1')) = h(op1('#skF_1','#skF_1')) )
| ~ sorti1(j(h('#skF_1')))
| ~ sorti2(h('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_1518,c_6082]) ).
tff(c_6292,plain,
op2(h('#skF_1'),h('#skF_1')) = h('#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_14,c_1518,c_10,c_6238]) ).
tff(c_83,plain,
! [W_25,X1_19] :
( ( h(op1(W_25,j(X1_19))) = op2(h(W_25),X1_19) )
| ~ sorti1(j(X1_19))
| ~ sorti1(W_25)
| ~ sorti2(X1_19) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_71]) ).
tff(c_1642,plain,
! [W_25] :
( ( op2(h(W_25),h('#skF_2')) = h(op1(W_25,'#skF_2')) )
| ~ sorti1(j(h('#skF_2')))
| ~ sorti1(W_25)
| ~ sorti2(h('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_1520,c_83]) ).
tff(c_3733,plain,
! [W_127] :
( ( op2(h(W_127),h('#skF_2')) = h(op1(W_127,'#skF_2')) )
| ~ sorti1(W_127) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_12,c_1520,c_1642]) ).
tff(c_6907,plain,
! [X1_154] :
( ( h(op1(j(X1_154),'#skF_2')) = op2(X1_154,h('#skF_2')) )
| ~ sorti1(j(X1_154))
| ~ sorti2(X1_154) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_3733]) ).
tff(c_7064,plain,
( ( op2(h('#skF_1'),h('#skF_2')) = h(op1('#skF_1','#skF_2')) )
| ~ sorti1(j(h('#skF_1')))
| ~ sorti2(h('#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_1518,c_6907]) ).
tff(c_7118,plain,
op2(h('#skF_1'),h('#skF_2')) = h(op1('#skF_1','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_14,c_1518,c_7064]) ).
tff(c_318,plain,
! [V_46] :
( ( op2(op2(V_46,V_46),V_46) = op2(V_46,V_46) )
| ( op2(op2(V_46,V_46),op2(V_46,V_46)) != V_46 )
| ~ sorti2(V_46)
| ~ sorti2(op2(V_46,V_46)) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_558,plain,
! [X_70] :
( ( op2(op2(h(X_70),h(X_70)),h(X_70)) = op2(h(X_70),h(X_70)) )
| ( op2(op2(h(X_70),h(X_70)),h(op1(X_70,X_70))) != h(X_70) )
| ~ sorti2(h(X_70))
| ~ sorti2(op2(h(X_70),h(X_70)))
| ~ sorti1(X_70)
| ~ sorti1(X_70) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_318]) ).
tff(c_595,plain,
( ( op2(op2(h('#skF_2'),h('#skF_2')),h('#skF_2')) = op2(h('#skF_2'),h('#skF_2')) )
| ( op2(op2(h('#skF_2'),h('#skF_2')),h('#skF_1')) != h('#skF_2') )
| ~ sorti2(h('#skF_2'))
| ~ sorti2(op2(h('#skF_2'),h('#skF_2')))
| ~ sorti1('#skF_2')
| ~ sorti1('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_558]) ).
tff(c_600,plain,
( ( op2(op2(h('#skF_2'),h('#skF_2')),h('#skF_2')) = op2(h('#skF_2'),h('#skF_2')) )
| ( op2(op2(h('#skF_2'),h('#skF_2')),h('#skF_1')) != h('#skF_2') )
| ~ sorti2(op2(h('#skF_2'),h('#skF_2'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_12,c_151,c_595]) ).
tff(c_9656,plain,
h(op1('#skF_1','#skF_2')) = h('#skF_1'),
inference(demodulation,[status(thm),theory(equality)],[c_150,c_5539,c_6292,c_5539,c_7118,c_5539,c_5539,c_600]) ).
tff(c_22,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_101]) ).
tff(c_1648,plain,
! [Y_16] :
( ( j(op2(Y_16,h('#skF_2'))) = op1(j(Y_16),'#skF_2') )
| ~ sorti2(h('#skF_2'))
| ~ sorti2(Y_16) ),
inference(superposition,[status(thm),theory(equality)],[c_1520,c_22]) ).
tff(c_1686,plain,
! [Y_16] :
( ( j(op2(Y_16,h('#skF_2'))) = op1(j(Y_16),'#skF_2') )
| ~ sorti2(Y_16) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_1648]) ).
tff(c_2445,plain,
( ( op1(j(h('#skF_1')),'#skF_2') = j(h(op1('#skF_1','#skF_2'))) )
| ~ sorti2(h('#skF_1'))
| ~ sorti1('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_2438,c_1686]) ).
tff(c_2531,plain,
j(h(op1('#skF_1','#skF_2'))) = op1('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_12,c_150,c_1518,c_2445]) ).
tff(c_9660,plain,
j(h('#skF_1')) = op1('#skF_1','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_9656,c_2531]) ).
tff(c_9663,plain,
op1('#skF_1','#skF_2') = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_1518,c_9660]) ).
tff(c_9665,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6,c_9663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG073+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 3 20:47:38 EDT 2023
% 0.16/0.34 % CPUTime :
% 8.31/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.31/3.08
% 8.31/3.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.31/3.12
% 8.31/3.12 Inference rules
% 8.31/3.12 ----------------------
% 8.31/3.12 #Ref : 0
% 8.31/3.12 #Sup : 2333
% 8.31/3.12 #Fact : 0
% 8.31/3.12 #Define : 0
% 8.31/3.12 #Split : 4
% 8.31/3.12 #Chain : 0
% 8.31/3.12 #Close : 0
% 8.31/3.12
% 8.31/3.12 Ordering : KBO
% 8.31/3.12
% 8.31/3.12 Simplification rules
% 8.31/3.12 ----------------------
% 8.31/3.12 #Subsume : 308
% 8.31/3.12 #Demod : 2980
% 8.31/3.12 #Tautology : 583
% 8.31/3.12 #SimpNegUnit : 1
% 8.31/3.12 #BackRed : 16
% 8.31/3.12
% 8.31/3.12 #Partial instantiations: 0
% 8.31/3.12 #Strategies tried : 1
% 8.31/3.12
% 8.31/3.12 Timing (in seconds)
% 8.31/3.12 ----------------------
% 8.31/3.12 Preprocessing : 0.47
% 8.31/3.12 Parsing : 0.26
% 8.31/3.12 CNF conversion : 0.03
% 8.31/3.12 Main loop : 1.65
% 8.31/3.12 Inferencing : 0.60
% 8.31/3.12 Reduction : 0.51
% 8.31/3.12 Demodulation : 0.37
% 8.31/3.12 BG Simplification : 0.07
% 8.31/3.12 Subsumption : 0.35
% 8.31/3.12 Abstraction : 0.08
% 8.31/3.12 MUC search : 0.00
% 8.31/3.12 Cooper : 0.00
% 8.31/3.13 Total : 2.18
% 8.31/3.13 Index Insertion : 0.00
% 8.31/3.13 Index Deletion : 0.00
% 8.31/3.13 Index Matching : 0.00
% 8.31/3.13 BG Taut test : 0.00
%------------------------------------------------------------------------------