%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:52:17 AM UTC 2026
% Result : Theorem 0.14s 0.76s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mNatSort,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> $true ),
file('theBenchmark.p',mNatSort) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('theBenchmark.p',mSortsC) ).
fof(mSortsC_01,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('theBenchmark.p',mSortsC_01) ).
fof(mSortsB,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('theBenchmark.p',mSortsB) ).
fof(mSortsB_02,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('theBenchmark.p',mSortsB_02) ).
fof(mAddComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ),
file('theBenchmark.p',mAddAsso) ).
fof(m_AddZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('theBenchmark.p',m_AddZero) ).
fof(mMulComm,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('theBenchmark.p',mMulComm) ).
fof(mMulAsso,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('theBenchmark.p',mMulAsso) ).
fof(m_MulUnit,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('theBenchmark.p',m_MulUnit) ).
fof(m_MulZero,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('theBenchmark.p',m_MulZero) ).
fof(mAMDistr,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('theBenchmark.p',mAMDistr) ).
fof(mAddCanc,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('theBenchmark.p',mAddCanc) ).
fof(mMulCanc,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 != sz00
=> ! [W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0)
| sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
=> W1 = W2 ) ) ) ),
file('theBenchmark.p',mMulCanc) ).
fof(mZeroAdd,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtpldt0(W0,W1) = sz00
=> ( W1 = sz00
& W0 = sz00 ) ) ),
file('theBenchmark.p',mZeroAdd) ).
fof(m__624,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('theBenchmark.p',m__624) ).
fof(m__,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xn = sz00
| xm = sz00 ) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mNatSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aNaturalNumber0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aNaturalNumber0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aNaturalNumber0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
aNaturalNumber0(sz00),
inference(fof_nnf,[status(thm)],[mSortsC]) ).
cnf(f_2_2,plain,
aNaturalNumber0(sz00),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(fof_nnf,[status(thm)],[mSortsC_01]) ).
cnf(f_3_2,plain,
aNaturalNumber0(sz10),
inference(clausify,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
sz10 != sz00,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [W0,W1] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB]) ).
fof(f_4_2,plain,
! [U_2,U_1] :
( aNaturalNumber0(sdtpldt0(U_2,U_1))
| ~ aNaturalNumber0(U_1)
| ~ aNaturalNumber0(U_2) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( aNaturalNumber0(sdtpldt0(U_2,U_1))
| ~ aNaturalNumber0(U_1)
| ~ aNaturalNumber0(U_2) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mSortsB_02]) ).
fof(f_5_2,plain,
! [U_4,U_3] :
( aNaturalNumber0(sdtasdt0(U_4,U_3))
| ~ aNaturalNumber0(U_3)
| ~ aNaturalNumber0(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( aNaturalNumber0(sdtasdt0(U_4,U_3))
| ~ aNaturalNumber0(U_3)
| ~ aNaturalNumber0(U_4) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAddComm]) ).
fof(f_6_2,plain,
! [U_6,U_5] :
( sdtpldt0(U_6,U_5) = sdtpldt0(U_5,U_6)
| ~ aNaturalNumber0(U_5)
| ~ aNaturalNumber0(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( sdtpldt0(U_6,U_5) = sdtpldt0(U_5,U_6)
| ~ aNaturalNumber0(U_5)
| ~ aNaturalNumber0(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [W0,W1,W2] :
( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAddAsso]) ).
fof(f_7_2,plain,
! [U_9,U_8,U_7] :
( sdtpldt0(sdtpldt0(U_9,U_8),U_7) = sdtpldt0(U_9,sdtpldt0(U_8,U_7))
| ~ aNaturalNumber0(U_7)
| ~ aNaturalNumber0(U_8)
| ~ aNaturalNumber0(U_9) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( sdtpldt0(sdtpldt0(U_9,U_8),U_7) = sdtpldt0(U_9,sdtpldt0(U_8,U_7))
| ~ aNaturalNumber0(U_7)
| ~ aNaturalNumber0(U_8)
| ~ aNaturalNumber0(U_9) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_AddZero]) ).
fof(f_8_2,plain,
! [U_10] :
( ( U_10 = sdtpldt0(sz00,U_10)
& sdtpldt0(U_10,sz00) = U_10 )
| ~ aNaturalNumber0(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( sdtpldt0(U_10,sz00) = U_10
| ~ aNaturalNumber0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_10 = sdtpldt0(sz00,U_10)
| ~ aNaturalNumber0(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMulComm]) ).
fof(f_9_2,plain,
! [U_12,U_11] :
( sdtasdt0(U_12,U_11) = sdtasdt0(U_11,U_12)
| ~ aNaturalNumber0(U_11)
| ~ aNaturalNumber0(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( sdtasdt0(U_12,U_11) = sdtasdt0(U_11,U_12)
| ~ aNaturalNumber0(U_11)
| ~ aNaturalNumber0(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMulAsso]) ).
fof(f_10_2,plain,
! [U_15,U_14,U_13] :
( sdtasdt0(sdtasdt0(U_15,U_14),U_13) = sdtasdt0(U_15,sdtasdt0(U_14,U_13))
| ~ aNaturalNumber0(U_13)
| ~ aNaturalNumber0(U_14)
| ~ aNaturalNumber0(U_15) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( sdtasdt0(sdtasdt0(U_15,U_14),U_13) = sdtasdt0(U_15,sdtasdt0(U_14,U_13))
| ~ aNaturalNumber0(U_13)
| ~ aNaturalNumber0(U_14)
| ~ aNaturalNumber0(U_15) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_MulUnit]) ).
fof(f_11_2,plain,
! [U_16] :
( ( U_16 = sdtasdt0(sz10,U_16)
& sdtasdt0(U_16,sz10) = U_16 )
| ~ aNaturalNumber0(U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( sdtasdt0(U_16,sz10) = U_16
| ~ aNaturalNumber0(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( U_16 = sdtasdt0(sz10,U_16)
| ~ aNaturalNumber0(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[m_MulZero]) ).
fof(f_12_2,plain,
! [U_17] :
( ( sz00 = sdtasdt0(sz00,U_17)
& sdtasdt0(U_17,sz00) = sz00 )
| ~ aNaturalNumber0(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( sdtasdt0(U_17,sz00) = sz00
| ~ aNaturalNumber0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( sz00 = sdtasdt0(sz00,U_17)
| ~ aNaturalNumber0(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAMDistr]) ).
fof(f_13_2,plain,
! [U_20,U_19,U_18] :
( ( sdtasdt0(sdtpldt0(U_19,U_18),U_20) = sdtpldt0(sdtasdt0(U_19,U_20),sdtasdt0(U_18,U_20))
& sdtasdt0(U_20,sdtpldt0(U_19,U_18)) = sdtpldt0(sdtasdt0(U_20,U_19),sdtasdt0(U_20,U_18)) )
| ~ aNaturalNumber0(U_18)
| ~ aNaturalNumber0(U_19)
| ~ aNaturalNumber0(U_20) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( sdtasdt0(U_20,sdtpldt0(U_19,U_18)) = sdtpldt0(sdtasdt0(U_20,U_19),sdtasdt0(U_20,U_18))
| ~ aNaturalNumber0(U_18)
| ~ aNaturalNumber0(U_19)
| ~ aNaturalNumber0(U_20) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( sdtasdt0(sdtpldt0(U_19,U_18),U_20) = sdtpldt0(sdtasdt0(U_19,U_20),sdtasdt0(U_18,U_20))
| ~ aNaturalNumber0(U_18)
| ~ aNaturalNumber0(U_19)
| ~ aNaturalNumber0(U_20) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mAddCanc]) ).
fof(f_14_2,plain,
! [U_23,U_22,U_21] :
( U_22 = U_21
| ( sdtpldt0(U_22,U_23) != sdtpldt0(U_21,U_23)
& sdtpldt0(U_23,U_22) != sdtpldt0(U_23,U_21) )
| ~ aNaturalNumber0(U_21)
| ~ aNaturalNumber0(U_22)
| ~ aNaturalNumber0(U_23) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( sdtpldt0(U_23,U_22) != sdtpldt0(U_23,U_21)
| U_22 = U_21
| ~ aNaturalNumber0(U_21)
| ~ aNaturalNumber0(U_22)
| ~ aNaturalNumber0(U_23) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( sdtpldt0(U_22,U_23) != sdtpldt0(U_21,U_23)
| U_22 = U_21
| ~ aNaturalNumber0(U_21)
| ~ aNaturalNumber0(U_22)
| ~ aNaturalNumber0(U_23) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [W0] :
( ! [W1,W2] :
( W1 = W2
| ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0)
& sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
| W0 = sz00
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mMulCanc]) ).
fof(f_15_2,plain,
! [U_26] :
( ! [U_25,U_24] :
( U_25 = U_24
| ( sdtasdt0(U_25,U_26) != sdtasdt0(U_24,U_26)
& sdtasdt0(U_26,U_25) != sdtasdt0(U_26,U_24) )
| ~ aNaturalNumber0(U_24)
| ~ aNaturalNumber0(U_25) )
| U_26 = sz00
| ~ aNaturalNumber0(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( sdtasdt0(U_26,U_25) != sdtasdt0(U_26,U_24)
| U_25 = U_24
| ~ aNaturalNumber0(U_24)
| ~ aNaturalNumber0(U_25)
| U_26 = sz00
| ~ aNaturalNumber0(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( sdtasdt0(U_25,U_26) != sdtasdt0(U_24,U_26)
| U_25 = U_24
| ~ aNaturalNumber0(U_24)
| ~ aNaturalNumber0(U_25)
| U_26 = sz00
| ~ aNaturalNumber0(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [W0,W1] :
( ( W1 = sz00
& W0 = sz00 )
| sdtpldt0(W0,W1) != sz00
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(fof_nnf,[status(thm)],[mZeroAdd]) ).
fof(f_16_2,plain,
! [U_28,U_27] :
( ( U_27 = sz00
& U_28 = sz00 )
| sdtpldt0(U_28,U_27) != sz00
| ~ aNaturalNumber0(U_27)
| ~ aNaturalNumber0(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( U_28 = sz00
| sdtpldt0(U_28,U_27) != sz00
| ~ aNaturalNumber0(U_27)
| ~ aNaturalNumber0(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( U_27 = sz00
| sdtpldt0(U_28,U_27) != sz00
| ~ aNaturalNumber0(U_27)
| ~ aNaturalNumber0(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
inference(fof_nnf,[status(thm)],[m__624]) ).
cnf(f_17_2,plain,
aNaturalNumber0(xm),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
aNaturalNumber0(xn),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,negated_conjecture,
( ~ ( xn = sz00
| xm = sz00 )
& sdtasdt0(xm,xn) = sz00 ),
inference(negate,[status(cth)],[m__]) ).
fof(f_18_2,negated_conjecture,
( xn != sz00
& xm != sz00
& sdtasdt0(xm,xn) = sz00 ),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
( xn != sz00
& xm != sz00
& sdtasdt0(xm,xn) = sz00 ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,negated_conjecture,
sdtasdt0(xm,xn) = sz00,
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,negated_conjecture,
xm != sz00,
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,negated_conjecture,
xn != sz00,
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( sdtpldt0(Eq_x_0,Eq_x_1) = sdtpldt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sdtasdt0(Eq_x_0,Eq_x_1) = sdtasdt0(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( aNaturalNumber0(Eq_y_0)
| ~ aNaturalNumber0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n019.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Sat Sep 19 18:29:37 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.14/0.76 % SZS status Theorem for theBenchmark
% 0.14/0.76 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------