TSTP Solution File: ALG071+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ALG071+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 : n001.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 33.69s 14.67s
% Output : CNFRefutation 33.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 13
% Syntax : Number of formulae : 132 ( 29 unt; 8 typ; 0 def)
% Number of atoms : 454 ( 94 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 654 ( 324 ~; 307 |; 8 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 7 >; 2 *; 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 : 137 (; 135 !; 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_60,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( sorti2(V)
& ( op2(V,op2(V,U)) != U )
& ( op2(U,op2(V,U)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
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/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_49,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( sorti1(V)
& ( op1(V,op1(V,U)) != U )
& ( op1(U,op1(V,U)) = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
tff(f_32,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(c_14,plain,
sorti2('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_24,plain,
! [V_12] :
( sorti1(j(V_12))
| ~ sorti2(V_12) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_26,plain,
! [U_11] :
( sorti2(h(U_11))
| ~ sorti1(U_11) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
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_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_16,plain,
! [X2_20] :
( ( j(h(X2_20)) = X2_20 )
| ~ sorti1(X2_20) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_76,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_97]) ).
tff(c_159,plain,
! [X2_43,Z_44] :
( ( j(op2(h(X2_43),Z_44)) = op1(X2_43,j(Z_44)) )
| ~ sorti2(Z_44)
| ~ sorti2(h(X2_43))
| ~ sorti1(X2_43) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_76]) ).
tff(c_18,plain,
! [X1_19] :
( ( h(j(X1_19)) = X1_19 )
| ~ sorti2(X1_19) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_582,plain,
! [X2_77,Z_78] :
( ( h(op1(X2_77,j(Z_78))) = op2(h(X2_77),Z_78) )
| ~ sorti2(op2(h(X2_77),Z_78))
| ~ sorti2(Z_78)
| ~ sorti2(h(X2_77))
| ~ sorti1(X2_77) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_18]) ).
tff(c_609,plain,
! [X2_79,V_80] :
( ( h(op1(X2_79,j(V_80))) = op2(h(X2_79),V_80) )
| ~ sorti1(X2_79)
| ~ sorti2(V_80)
| ~ sorti2(h(X2_79)) ),
inference(resolution,[status(thm)],[c_4,c_582]) ).
tff(c_1856,plain,
! [Y_117,Z_118] :
( ( op2(h(j(Y_117)),Z_118) = h(j(op2(Y_117,Z_118))) )
| ~ sorti1(j(Y_117))
| ~ sorti2(Z_118)
| ~ sorti2(h(j(Y_117)))
| ~ sorti2(Z_118)
| ~ sorti2(Y_117) ),
inference(superposition,[status(thm),theory(equality)],[c_20,c_609]) ).
tff(c_1881,plain,
! [Y_117,Z_118] :
( ( op2(h(j(Y_117)),Z_118) = h(j(op2(Y_117,Z_118))) )
| ~ sorti2(Z_118)
| ~ sorti2(Y_117)
| ~ sorti1(j(Y_117)) ),
inference(resolution,[status(thm)],[c_26,c_1856]) ).
tff(c_1882,plain,
! [Y_119,Z_120] :
( ( op2(h(j(Y_119)),Z_120) = h(j(op2(Y_119,Z_120))) )
| ~ sorti2(Z_120)
| ~ sorti2(Y_119)
| ~ sorti1(j(Y_119)) ),
inference(resolution,[status(thm)],[c_26,c_1856]) ).
tff(c_1970,plain,
! [X1_19,Z_120] :
( ( h(j(op2(X1_19,Z_120))) = op2(X1_19,Z_120) )
| ~ sorti2(Z_120)
| ~ sorti2(X1_19)
| ~ sorti1(j(X1_19))
| ~ sorti2(X1_19) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_1882]) ).
tff(c_12,plain,
! [V_10] :
( ( op2('#skF_2',op2(V_10,'#skF_2')) != V_10 )
| ( op2(V_10,op2(V_10,'#skF_2')) = '#skF_2' )
| ~ sorti2(V_10) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_1925,plain,
! [Y_119] :
( ( op2('#skF_2',h(j(op2(Y_119,'#skF_2')))) != h(j(Y_119)) )
| ( op2(h(j(Y_119)),op2(h(j(Y_119)),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(Y_119)))
| ~ sorti2('#skF_2')
| ~ sorti2(Y_119)
| ~ sorti1(j(Y_119)) ),
inference(superposition,[status(thm),theory(equality)],[c_1882,c_12]) ).
tff(c_27710,plain,
! [Y_504] :
( ( op2('#skF_2',h(j(op2(Y_504,'#skF_2')))) != h(j(Y_504)) )
| ( op2(h(j(Y_504)),op2(h(j(Y_504)),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(Y_504)))
| ~ sorti2(Y_504)
| ~ sorti1(j(Y_504)) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_1925]) ).
tff(c_30878,plain,
! [X1_541] :
( ( op2('#skF_2',h(j(op2(X1_541,'#skF_2')))) != h(j(X1_541)) )
| ( op2(X1_541,op2(h(j(X1_541)),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(X1_541)))
| ~ sorti2(X1_541)
| ~ sorti1(j(X1_541))
| ~ sorti2(X1_541) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_27710]) ).
tff(c_30902,plain,
! [X1_19] :
( ( op2('#skF_2',op2(X1_19,'#skF_2')) != h(j(X1_19)) )
| ( op2(X1_19,op2(h(j(X1_19)),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(X1_19)))
| ~ sorti2(X1_19)
| ~ sorti1(j(X1_19))
| ~ sorti2(X1_19)
| ~ sorti2('#skF_2')
| ~ sorti2(X1_19)
| ~ sorti1(j(X1_19))
| ~ sorti2(X1_19) ),
inference(superposition,[status(thm),theory(equality)],[c_1970,c_30878]) ).
tff(c_30937,plain,
! [X1_542] :
( ( op2('#skF_2',op2(X1_542,'#skF_2')) != h(j(X1_542)) )
| ( op2(X1_542,op2(h(j(X1_542)),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(X1_542)))
| ~ sorti1(j(X1_542))
| ~ sorti2(X1_542) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_30902]) ).
tff(c_31269,plain,
! [Y_117] :
( ( op2('#skF_2',op2(Y_117,'#skF_2')) != h(j(Y_117)) )
| ( op2(Y_117,h(j(op2(Y_117,'#skF_2')))) = '#skF_2' )
| ~ sorti2(h(j(Y_117)))
| ~ sorti1(j(Y_117))
| ~ sorti2(Y_117)
| ~ sorti2('#skF_2')
| ~ sorti2(Y_117)
| ~ sorti1(j(Y_117)) ),
inference(superposition,[status(thm),theory(equality)],[c_1881,c_30937]) ).
tff(c_31583,plain,
! [Y_546] :
( ( op2('#skF_2',op2(Y_546,'#skF_2')) != h(j(Y_546)) )
| ( op2(Y_546,h(j(op2(Y_546,'#skF_2')))) = '#skF_2' )
| ~ sorti2(h(j(Y_546)))
| ~ sorti2(Y_546)
| ~ sorti1(j(Y_546)) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_31269]) ).
tff(c_28107,plain,
! [X1_19] :
( ( op2('#skF_2',h(j(op2(X1_19,'#skF_2')))) != h(j(X1_19)) )
| ( op2(X1_19,op2(h(j(X1_19)),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(X1_19)))
| ~ sorti2(X1_19)
| ~ sorti1(j(X1_19))
| ~ sorti2(X1_19) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_27710]) ).
tff(c_31589,plain,
( ( h(j('#skF_2')) != '#skF_2' )
| ( op2('#skF_2',op2(h(j('#skF_2')),'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j('#skF_2')))
| ~ sorti2('#skF_2')
| ~ sorti1(j('#skF_2'))
| ~ sorti2('#skF_2')
| ( op2('#skF_2',op2('#skF_2','#skF_2')) != h(j('#skF_2')) )
| ~ sorti2(h(j('#skF_2')))
| ~ sorti2('#skF_2')
| ~ sorti1(j('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_31583,c_28107]) ).
tff(c_31972,plain,
( ( h(j('#skF_2')) != '#skF_2' )
| ( op2('#skF_2',op2(h(j('#skF_2')),'#skF_2')) = '#skF_2' )
| ( op2('#skF_2',op2('#skF_2','#skF_2')) != h(j('#skF_2')) )
| ~ sorti2(h(j('#skF_2')))
| ~ sorti1(j('#skF_2')) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14,c_14,c_31589]) ).
tff(c_32003,plain,
~ sorti1(j('#skF_2')),
inference(splitLeft,[status(thm)],[c_31972]) ).
tff(c_32006,plain,
~ sorti2('#skF_2'),
inference(resolution,[status(thm)],[c_24,c_32003]) ).
tff(c_32010,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_32006]) ).
tff(c_32012,plain,
sorti1(j('#skF_2')),
inference(splitRight,[status(thm)],[c_31972]) ).
tff(c_10,plain,
! [U_7] :
( sorti1('#skF_1'(U_7))
| ~ sorti1(U_7) ),
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_95,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_97]) ).
tff(c_195,plain,
! [W_45,X1_46] :
( ( h(op1(W_45,j(X1_46))) = op2(h(W_45),X1_46) )
| ~ sorti1(j(X1_46))
| ~ sorti1(W_45)
| ~ sorti2(X1_46) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_95]) ).
tff(c_685,plain,
! [W_81,X1_82] :
( ( j(op2(h(W_81),X1_82)) = op1(W_81,j(X1_82)) )
| ~ sorti1(op1(W_81,j(X1_82)))
| ~ sorti1(j(X1_82))
| ~ sorti1(W_81)
| ~ sorti2(X1_82) ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_16]) ).
tff(c_714,plain,
! [U_1,X1_82] :
( ( j(op2(h(U_1),X1_82)) = op1(U_1,j(X1_82)) )
| ~ sorti2(X1_82)
| ~ sorti1(j(X1_82))
| ~ sorti1(U_1) ),
inference(resolution,[status(thm)],[c_2,c_685]) ).
tff(c_32011,plain,
( ~ sorti2(h(j('#skF_2')))
| ( op2('#skF_2',op2('#skF_2','#skF_2')) != h(j('#skF_2')) )
| ( h(j('#skF_2')) != '#skF_2' )
| ( op2('#skF_2',op2(h(j('#skF_2')),'#skF_2')) = '#skF_2' ) ),
inference(splitRight,[status(thm)],[c_31972]) ).
tff(c_32143,plain,
h(j('#skF_2')) != '#skF_2',
inference(splitLeft,[status(thm)],[c_32011]) ).
tff(c_32146,plain,
~ sorti2('#skF_2'),
inference(superposition,[status(thm),theory(equality)],[c_18,c_32143]) ).
tff(c_32150,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_32146]) ).
tff(c_32152,plain,
h(j('#skF_2')) = '#skF_2',
inference(splitRight,[status(thm)],[c_32011]) ).
tff(c_22,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_97]) ).
tff(c_32372,plain,
! [W_13] :
( ( h(op1(W_13,j('#skF_2'))) = op2(h(W_13),'#skF_2') )
| ~ sorti1(j('#skF_2'))
| ~ sorti1(W_13) ),
inference(superposition,[status(thm),theory(equality)],[c_32152,c_22]) ).
tff(c_36553,plain,
! [W_571] :
( ( h(op1(W_571,j('#skF_2'))) = op2(h(W_571),'#skF_2') )
| ~ sorti1(W_571) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_32372]) ).
tff(c_715,plain,
! [U_83,X1_84] :
( ( j(op2(h(U_83),X1_84)) = op1(U_83,j(X1_84)) )
| ~ sorti2(X1_84)
| ~ sorti1(j(X1_84))
| ~ sorti1(U_83) ),
inference(resolution,[status(thm)],[c_2,c_685]) ).
tff(c_1452,plain,
! [W_105,X_106] :
( ( op1(W_105,j(h(X_106))) = j(h(op1(W_105,X_106))) )
| ~ sorti2(h(X_106))
| ~ sorti1(j(h(X_106)))
| ~ sorti1(W_105)
| ~ sorti1(X_106)
| ~ sorti1(W_105) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_715]) ).
tff(c_1479,plain,
! [W_107,X_108] :
( ( op1(W_107,j(h(X_108))) = j(h(op1(W_107,X_108))) )
| ~ sorti1(X_108)
| ~ sorti1(W_107)
| ~ sorti2(h(X_108)) ),
inference(resolution,[status(thm)],[c_24,c_1452]) ).
tff(c_1537,plain,
! [W_107,X_108] :
( sorti1(j(h(op1(W_107,X_108))))
| ~ sorti1(j(h(X_108)))
| ~ sorti1(W_107)
| ~ sorti1(X_108)
| ~ sorti1(W_107)
| ~ sorti2(h(X_108)) ),
inference(superposition,[status(thm),theory(equality)],[c_1479,c_2]) ).
tff(c_36869,plain,
! [W_571] :
( sorti1(j(op2(h(W_571),'#skF_2')))
| ~ sorti1(j(h(j('#skF_2'))))
| ~ sorti1(W_571)
| ~ sorti1(j('#skF_2'))
| ~ sorti1(W_571)
| ~ sorti2(h(j('#skF_2')))
| ~ sorti1(W_571) ),
inference(superposition,[status(thm),theory(equality)],[c_36553,c_1537]) ).
tff(c_37254,plain,
! [W_573] :
( sorti1(j(op2(h(W_573),'#skF_2')))
| ~ sorti1(W_573) ),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_32152,c_32012,c_32012,c_32152,c_36869]) ).
tff(c_37342,plain,
! [U_1] :
( sorti1(op1(U_1,j('#skF_2')))
| ~ sorti1(U_1)
| ~ sorti2('#skF_2')
| ~ sorti1(j('#skF_2'))
| ~ sorti1(U_1) ),
inference(superposition,[status(thm),theory(equality)],[c_714,c_37254]) ).
tff(c_37371,plain,
! [U_574] :
( sorti1(op1(U_574,j('#skF_2')))
| ~ sorti1(U_574) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_14,c_37342]) ).
tff(c_6,plain,
! [U_7] :
( ( op1(U_7,op1('#skF_1'(U_7),U_7)) = '#skF_1'(U_7) )
| ~ sorti1(U_7) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_1665,plain,
! [W_111,X_112] :
( sorti1(j(h(op1(W_111,X_112))))
| ~ sorti1(j(h(X_112)))
| ~ sorti1(W_111)
| ~ sorti1(X_112)
| ~ sorti1(W_111)
| ~ sorti2(h(X_112)) ),
inference(superposition,[status(thm),theory(equality)],[c_1479,c_2]) ).
tff(c_28796,plain,
! [U_518] :
( sorti1(j(h('#skF_1'(U_518))))
| ~ sorti1(j(h(op1('#skF_1'(U_518),U_518))))
| ~ sorti1(U_518)
| ~ sorti1(op1('#skF_1'(U_518),U_518))
| ~ sorti1(U_518)
| ~ sorti2(h(op1('#skF_1'(U_518),U_518)))
| ~ sorti1(U_518) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_1665]) ).
tff(c_28875,plain,
! [U_519] :
( sorti1(j(h('#skF_1'(U_519))))
| ~ sorti1(op1('#skF_1'(U_519),U_519))
| ~ sorti1(U_519)
| ~ sorti2(h(op1('#skF_1'(U_519),U_519))) ),
inference(resolution,[status(thm)],[c_24,c_28796]) ).
tff(c_28924,plain,
! [U_519] :
( sorti1(j(h('#skF_1'(U_519))))
| ~ sorti1(U_519)
| ~ sorti1(op1('#skF_1'(U_519),U_519)) ),
inference(resolution,[status(thm)],[c_26,c_28875]) ).
tff(c_37374,plain,
( sorti1(j(h('#skF_1'(j('#skF_2')))))
| ~ sorti1(j('#skF_2'))
| ~ sorti1('#skF_1'(j('#skF_2'))) ),
inference(resolution,[status(thm)],[c_37371,c_28924]) ).
tff(c_37425,plain,
( sorti1(j(h('#skF_1'(j('#skF_2')))))
| ~ sorti1('#skF_1'(j('#skF_2'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_37374]) ).
tff(c_37456,plain,
~ sorti1('#skF_1'(j('#skF_2'))),
inference(splitLeft,[status(thm)],[c_37425]) ).
tff(c_37459,plain,
~ sorti1(j('#skF_2')),
inference(resolution,[status(thm)],[c_10,c_37456]) ).
tff(c_37463,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_37459]) ).
tff(c_37465,plain,
sorti1('#skF_1'(j('#skF_2'))),
inference(splitRight,[status(thm)],[c_37425]) ).
tff(c_37368,plain,
! [U_1] :
( sorti1(op1(U_1,j('#skF_2')))
| ~ sorti1(U_1) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_14,c_37342]) ).
tff(c_125,plain,
! [X1_41,X_42] :
( ( h(op1(j(X1_41),X_42)) = op2(X1_41,h(X_42)) )
| ~ sorti1(X_42)
| ~ sorti1(j(X1_41))
| ~ sorti2(X1_41) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_95]) ).
tff(c_153,plain,
! [X1_41] :
( ( op2(X1_41,h(op1('#skF_1'(j(X1_41)),j(X1_41)))) = h('#skF_1'(j(X1_41))) )
| ~ sorti1(op1('#skF_1'(j(X1_41)),j(X1_41)))
| ~ sorti1(j(X1_41))
| ~ sorti2(X1_41)
| ~ sorti1(j(X1_41)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_125]) ).
tff(c_32369,plain,
! [X_15] :
( ( h(op1(j('#skF_2'),X_15)) = op2('#skF_2',h(X_15)) )
| ~ sorti1(X_15)
| ~ sorti1(j('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_32152,c_22]) ).
tff(c_34964,plain,
! [X_563] :
( ( h(op1(j('#skF_2'),X_563)) = op2('#skF_2',h(X_563)) )
| ~ sorti1(X_563) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_32369]) ).
tff(c_289,plain,
! [X1_49,X_50] :
( sorti2(op2(X1_49,h(X_50)))
| ~ sorti1(op1(j(X1_49),X_50))
| ~ sorti1(X_50)
| ~ sorti1(j(X1_49))
| ~ sorti2(X1_49) ),
inference(superposition,[status(thm),theory(equality)],[c_125,c_26]) ).
tff(c_3457,plain,
! [W_159,X_160] :
( sorti2(h(op1(W_159,X_160)))
| ~ sorti1(op1(j(h(W_159)),X_160))
| ~ sorti1(X_160)
| ~ sorti1(j(h(W_159)))
| ~ sorti2(h(W_159))
| ~ sorti1(X_160)
| ~ sorti1(W_159) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_289]) ).
tff(c_3529,plain,
! [W_159,V_3] :
( sorti2(h(op1(W_159,V_3)))
| ~ sorti2(h(W_159))
| ~ sorti1(W_159)
| ~ sorti1(V_3)
| ~ sorti1(j(h(W_159))) ),
inference(resolution,[status(thm)],[c_2,c_3457]) ).
tff(c_35223,plain,
! [X_563] :
( sorti2(op2('#skF_2',h(X_563)))
| ~ sorti2(h(j('#skF_2')))
| ~ sorti1(j('#skF_2'))
| ~ sorti1(X_563)
| ~ sorti1(j(h(j('#skF_2'))))
| ~ sorti1(X_563) ),
inference(superposition,[status(thm),theory(equality)],[c_34964,c_3529]) ).
tff(c_35652,plain,
! [X_565] :
( sorti2(op2('#skF_2',h(X_565)))
| ~ sorti1(X_565) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_32152,c_32012,c_14,c_32152,c_35223]) ).
tff(c_35713,plain,
( sorti2(h('#skF_1'(j('#skF_2'))))
| ~ sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2')))
| ~ sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2')))
| ~ sorti1(j('#skF_2'))
| ~ sorti2('#skF_2')
| ~ sorti1(j('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_153,c_35652]) ).
tff(c_35760,plain,
( sorti2(h('#skF_1'(j('#skF_2'))))
| ~ sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_14,c_32012,c_35713]) ).
tff(c_51043,plain,
~ sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2'))),
inference(splitLeft,[status(thm)],[c_35760]) ).
tff(c_51046,plain,
~ sorti1('#skF_1'(j('#skF_2'))),
inference(resolution,[status(thm)],[c_37368,c_51043]) ).
tff(c_51056,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_37465,c_51046]) ).
tff(c_51057,plain,
sorti2(h('#skF_1'(j('#skF_2')))),
inference(splitRight,[status(thm)],[c_35760]) ).
tff(c_302,plain,
! [W_51,X1_52] :
( sorti2(op2(h(W_51),X1_52))
| ~ sorti1(op1(W_51,j(X1_52)))
| ~ sorti1(j(X1_52))
| ~ sorti1(W_51)
| ~ sorti2(X1_52) ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_26]) ).
tff(c_3363,plain,
! [W_155,X_156] :
( sorti2(h(op1(W_155,X_156)))
| ~ sorti1(op1(W_155,j(h(X_156))))
| ~ sorti1(j(h(X_156)))
| ~ sorti1(W_155)
| ~ sorti2(h(X_156))
| ~ sorti1(X_156)
| ~ sorti1(W_155) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_302]) ).
tff(c_3431,plain,
! [U_1,X_156] :
( sorti2(h(op1(U_1,X_156)))
| ~ sorti2(h(X_156))
| ~ sorti1(X_156)
| ~ sorti1(j(h(X_156)))
| ~ sorti1(U_1) ),
inference(resolution,[status(thm)],[c_2,c_3363]) ).
tff(c_1575,plain,
! [W_109,X2_110] :
( ( j(h(op1(W_109,X2_110))) = op1(W_109,X2_110) )
| ~ sorti1(X2_110)
| ~ sorti1(W_109)
| ~ sorti2(h(X2_110))
| ~ sorti1(X2_110) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_1479]) ).
tff(c_359,plain,
! [X2_57,Z_58] :
( sorti1(op1(X2_57,j(Z_58)))
| ~ sorti2(op2(h(X2_57),Z_58))
| ~ sorti2(Z_58)
| ~ sorti2(h(X2_57))
| ~ sorti1(X2_57) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_24]) ).
tff(c_385,plain,
! [X2_57,V_6] :
( sorti1(op1(X2_57,j(V_6)))
| ~ sorti1(X2_57)
| ~ sorti2(V_6)
| ~ sorti2(h(X2_57)) ),
inference(resolution,[status(thm)],[c_4,c_359]) ).
tff(c_6221,plain,
! [X2_238,W_239,X2_240] :
( sorti1(op1(X2_238,op1(W_239,X2_240)))
| ~ sorti1(X2_238)
| ~ sorti2(h(op1(W_239,X2_240)))
| ~ sorti2(h(X2_238))
| ~ sorti1(X2_240)
| ~ sorti1(W_239)
| ~ sorti2(h(X2_240))
| ~ sorti1(X2_240) ),
inference(superposition,[status(thm),theory(equality)],[c_1575,c_385]) ).
tff(c_6260,plain,
! [X2_238,U_1,X_156] :
( sorti1(op1(X2_238,op1(U_1,X_156)))
| ~ sorti1(X2_238)
| ~ sorti2(h(X2_238))
| ~ sorti2(h(X_156))
| ~ sorti1(X_156)
| ~ sorti1(j(h(X_156)))
| ~ sorti1(U_1) ),
inference(resolution,[status(thm)],[c_3431,c_6221]) ).
tff(c_51058,plain,
sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2'))),
inference(splitRight,[status(thm)],[c_35760]) ).
tff(c_399,plain,
! [X1_61,X_62] :
( ( j(op2(X1_61,h(X_62))) = op1(j(X1_61),X_62) )
| ~ sorti1(op1(j(X1_61),X_62))
| ~ sorti1(X_62)
| ~ sorti1(j(X1_61))
| ~ sorti2(X1_61) ),
inference(superposition,[status(thm),theory(equality)],[c_125,c_16]) ).
tff(c_430,plain,
! [X1_63,V_64] :
( ( j(op2(X1_63,h(V_64))) = op1(j(X1_63),V_64) )
| ~ sorti2(X1_63)
| ~ sorti1(V_64)
| ~ sorti1(j(X1_63)) ),
inference(resolution,[status(thm)],[c_2,c_399]) ).
tff(c_2758,plain,
! [W_139,X_140] :
( ( op1(j(h(W_139)),X_140) = j(h(op1(W_139,X_140))) )
| ~ sorti2(h(W_139))
| ~ sorti1(X_140)
| ~ sorti1(j(h(W_139)))
| ~ sorti1(X_140)
| ~ sorti1(W_139) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_430]) ).
tff(c_2799,plain,
! [W_141,X_142] :
( ( op1(j(h(W_141)),X_142) = j(h(op1(W_141,X_142))) )
| ~ sorti1(X_142)
| ~ sorti1(W_141)
| ~ sorti2(h(W_141)) ),
inference(resolution,[status(thm)],[c_24,c_2758]) ).
tff(c_2914,plain,
! [X2_143,X_144] :
( ( j(h(op1(X2_143,X_144))) = op1(X2_143,X_144) )
| ~ sorti1(X_144)
| ~ sorti1(X2_143)
| ~ sorti2(h(X2_143))
| ~ sorti1(X2_143) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_2799]) ).
tff(c_3020,plain,
! [U_7] :
( ( op1(U_7,op1('#skF_1'(U_7),U_7)) = j(h('#skF_1'(U_7))) )
| ~ sorti1(op1('#skF_1'(U_7),U_7))
| ~ sorti1(U_7)
| ~ sorti2(h(U_7))
| ~ sorti1(U_7)
| ~ sorti1(U_7) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_2914]) ).
tff(c_51068,plain,
( ( op1(j('#skF_2'),op1('#skF_1'(j('#skF_2')),j('#skF_2'))) = j(h('#skF_1'(j('#skF_2')))) )
| ~ sorti2(h(j('#skF_2')))
| ~ sorti1(j('#skF_2')) ),
inference(resolution,[status(thm)],[c_51058,c_3020]) ).
tff(c_51083,plain,
op1(j('#skF_2'),op1('#skF_1'(j('#skF_2')),j('#skF_2'))) = j(h('#skF_1'(j('#skF_2')))),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_14,c_32152,c_51068]) ).
tff(c_77056,plain,
( ( j(h('#skF_1'(j('#skF_2')))) = '#skF_1'(j('#skF_2')) )
| ~ sorti1(j('#skF_2')) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_51083]) ).
tff(c_77250,plain,
j(h('#skF_1'(j('#skF_2')))) = '#skF_1'(j('#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_77056]) ).
tff(c_78112,plain,
op1(j('#skF_2'),op1('#skF_1'(j('#skF_2')),j('#skF_2'))) = '#skF_1'(j('#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_77250,c_51083]) ).
tff(c_6050,plain,
! [W_235,W_236,X1_237] :
( ( op2(h(W_235),op2(h(W_236),X1_237)) = h(op1(W_235,op1(W_236,j(X1_237)))) )
| ~ sorti1(op1(W_236,j(X1_237)))
| ~ sorti1(W_235)
| ~ sorti1(j(X1_237))
| ~ sorti1(W_236)
| ~ sorti2(X1_237) ),
inference(superposition,[status(thm),theory(equality)],[c_195,c_22]) ).
tff(c_6215,plain,
! [X1_19,W_236,X1_237] :
( ( h(op1(j(X1_19),op1(W_236,j(X1_237)))) = op2(X1_19,op2(h(W_236),X1_237)) )
| ~ sorti1(op1(W_236,j(X1_237)))
| ~ sorti1(j(X1_19))
| ~ sorti1(j(X1_237))
| ~ sorti1(W_236)
| ~ sorti2(X1_237)
| ~ sorti2(X1_19) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_6050]) ).
tff(c_78771,plain,
( ( op2('#skF_2',op2(h('#skF_1'(j('#skF_2'))),'#skF_2')) = h('#skF_1'(j('#skF_2'))) )
| ~ sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2')))
| ~ sorti1(j('#skF_2'))
| ~ sorti1(j('#skF_2'))
| ~ sorti1('#skF_1'(j('#skF_2')))
| ~ sorti2('#skF_2')
| ~ sorti2('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_78112,c_6215]) ).
tff(c_79043,plain,
op2('#skF_2',op2(h('#skF_1'(j('#skF_2'))),'#skF_2')) = h('#skF_1'(j('#skF_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_14,c_14,c_37465,c_32012,c_32012,c_51058,c_78771]) ).
tff(c_31333,plain,
! [X1_543] :
( ( op2('#skF_2',op2(X1_543,'#skF_2')) != h(j(X1_543)) )
| ( op2(X1_543,op2(X1_543,'#skF_2')) = '#skF_2' )
| ~ sorti2(h(j(X1_543)))
| ~ sorti1(j(X1_543))
| ~ sorti2(X1_543)
| ~ sorti2(X1_543) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_30937]) ).
tff(c_31458,plain,
! [X1_544] :
( ( op2('#skF_2',op2(X1_544,'#skF_2')) != h(j(X1_544)) )
| ( op2(X1_544,op2(X1_544,'#skF_2')) = '#skF_2' )
| ~ sorti2(X1_544)
| ~ sorti1(j(X1_544)) ),
inference(resolution,[status(thm)],[c_26,c_31333]) ).
tff(c_31566,plain,
! [V_12] :
( ( op2('#skF_2',op2(V_12,'#skF_2')) != h(j(V_12)) )
| ( op2(V_12,op2(V_12,'#skF_2')) = '#skF_2' )
| ~ sorti2(V_12) ),
inference(resolution,[status(thm)],[c_24,c_31458]) ).
tff(c_80911,plain,
( ( h(j(h('#skF_1'(j('#skF_2'))))) != h('#skF_1'(j('#skF_2'))) )
| ( op2(h('#skF_1'(j('#skF_2'))),op2(h('#skF_1'(j('#skF_2'))),'#skF_2')) = '#skF_2' )
| ~ sorti2(h('#skF_1'(j('#skF_2')))) ),
inference(superposition,[status(thm),theory(equality)],[c_79043,c_31566]) ).
tff(c_81048,plain,
op2(h('#skF_1'(j('#skF_2'))),op2(h('#skF_1'(j('#skF_2'))),'#skF_2')) = '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_51057,c_77250,c_80911]) ).
tff(c_36922,plain,
! [W_13,W_571] :
( ( op2(h(W_13),op2(h(W_571),'#skF_2')) = h(op1(W_13,op1(W_571,j('#skF_2')))) )
| ~ sorti1(op1(W_571,j('#skF_2')))
| ~ sorti1(W_13)
| ~ sorti1(W_571) ),
inference(superposition,[status(thm),theory(equality)],[c_36553,c_22]) ).
tff(c_81131,plain,
( ( h(op1('#skF_1'(j('#skF_2')),op1('#skF_1'(j('#skF_2')),j('#skF_2')))) = '#skF_2' )
| ~ sorti1(op1('#skF_1'(j('#skF_2')),j('#skF_2')))
| ~ sorti1('#skF_1'(j('#skF_2')))
| ~ sorti1('#skF_1'(j('#skF_2'))) ),
inference(superposition,[status(thm),theory(equality)],[c_81048,c_36922]) ).
tff(c_81316,plain,
h(op1('#skF_1'(j('#skF_2')),op1('#skF_1'(j('#skF_2')),j('#skF_2')))) = '#skF_2',
inference(demodulation,[status(thm),theory(equality)],[c_37465,c_37465,c_51058,c_81131]) ).
tff(c_81838,plain,
( ( op1('#skF_1'(j('#skF_2')),op1('#skF_1'(j('#skF_2')),j('#skF_2'))) = j('#skF_2') )
| ~ sorti1(op1('#skF_1'(j('#skF_2')),op1('#skF_1'(j('#skF_2')),j('#skF_2')))) ),
inference(superposition,[status(thm),theory(equality)],[c_81316,c_16]) ).
tff(c_82016,plain,
~ sorti1(op1('#skF_1'(j('#skF_2')),op1('#skF_1'(j('#skF_2')),j('#skF_2')))),
inference(splitLeft,[status(thm)],[c_81838]) ).
tff(c_82025,plain,
( ~ sorti2(h('#skF_1'(j('#skF_2'))))
| ~ sorti2(h(j('#skF_2')))
| ~ sorti1(j('#skF_2'))
| ~ sorti1(j(h(j('#skF_2'))))
| ~ sorti1('#skF_1'(j('#skF_2'))) ),
inference(resolution,[status(thm)],[c_6260,c_82016]) ).
tff(c_82050,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_37465,c_32012,c_32152,c_32012,c_14,c_32152,c_51057,c_82025]) ).
tff(c_82051,plain,
op1('#skF_1'(j('#skF_2')),op1('#skF_1'(j('#skF_2')),j('#skF_2'))) = j('#skF_2'),
inference(splitRight,[status(thm)],[c_81838]) ).
tff(c_8,plain,
! [U_7] :
( ( op1('#skF_1'(U_7),op1('#skF_1'(U_7),U_7)) != U_7 )
| ~ sorti1(U_7) ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_82196,plain,
~ sorti1(j('#skF_2')),
inference(superposition,[status(thm),theory(equality)],[c_82051,c_8]) ).
tff(c_82295,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_32012,c_82196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG071+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
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 3 20:48:25 EDT 2023
% 0.14/0.33 % CPUTime :
% 33.69/14.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.69/14.68
% 33.69/14.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.69/14.73
% 33.69/14.73 Inference rules
% 33.69/14.73 ----------------------
% 33.69/14.73 #Ref : 0
% 33.69/14.73 #Sup : 23089
% 33.69/14.73 #Fact : 0
% 33.69/14.73 #Define : 0
% 33.69/14.73 #Split : 5
% 33.69/14.73 #Chain : 0
% 33.69/14.73 #Close : 0
% 33.69/14.73
% 33.69/14.73 Ordering : KBO
% 33.69/14.73
% 33.69/14.73 Simplification rules
% 33.69/14.73 ----------------------
% 33.69/14.73 #Subsume : 3374
% 33.69/14.73 #Demod : 14581
% 33.69/14.73 #Tautology : 1796
% 33.69/14.73 #SimpNegUnit : 0
% 33.69/14.73 #BackRed : 9
% 33.69/14.73
% 33.69/14.73 #Partial instantiations: 0
% 33.69/14.73 #Strategies tried : 1
% 33.69/14.73
% 33.69/14.73 Timing (in seconds)
% 33.69/14.73 ----------------------
% 33.69/14.73 Preprocessing : 0.48
% 33.69/14.73 Parsing : 0.26
% 33.69/14.73 CNF conversion : 0.03
% 33.69/14.74 Main loop : 13.21
% 33.69/14.74 Inferencing : 2.93
% 33.69/14.74 Reduction : 2.96
% 33.69/14.74 Demodulation : 2.61
% 33.69/14.74 BG Simplification : 0.40
% 33.69/14.74 Subsumption : 5.88
% 33.69/14.74 Abstraction : 0.49
% 33.69/14.74 MUC search : 0.00
% 33.69/14.74 Cooper : 0.00
% 33.69/14.74 Total : 13.76
% 33.69/14.74 Index Insertion : 0.00
% 33.69/14.74 Index Deletion : 0.00
% 33.69/14.74 Index Matching : 0.00
% 33.69/14.74 BG Taut test : 0.00
%------------------------------------------------------------------------------