%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM016+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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 08:14:44 AM UTC 2026
% Result : Theorem 30.70s 31.11s
% Output : Proof 30.70s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
file('theBenchmark.p',mElmSort) ).
fof(mRelSort,axiom,
! [W0] :
( aRewritingSystem0(W0)
=> $true ),
file('theBenchmark.p',mRelSort) ).
fof(mReduct,axiom,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('theBenchmark.p',mReduct) ).
fof(mWFOrd,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( iLess0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mWFOrd) ).
fof(mTCbr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
=> $true ) ),
file('theBenchmark.p',mTCbr) ).
fof(mTCDef,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1) ) ) ),
file('theBenchmark.p',mTCDef) ).
fof(mTCTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W2,W1,W3)
& sdtmndtplgtdt0(W0,W1,W2) )
=> sdtmndtplgtdt0(W0,W1,W3) ) ),
file('theBenchmark.p',mTCTrans) ).
fof(mTCRDef,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2 ) ) ),
file('theBenchmark.p',mTCRDef) ).
fof(mTCRTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtasgtdt0(W2,W1,W3)
& sdtmndtasgtdt0(W0,W1,W2) )
=> sdtmndtasgtdt0(W0,W1,W3) ) ),
file('theBenchmark.p',mTCRTrans) ).
fof(mCRDef,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( sdtmndtasgtdt0(W1,W0,W3)
& sdtmndtasgtdt0(W1,W0,W2)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
=> ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) ) ) ) ),
file('theBenchmark.p',mCRDef) ).
fof(mWCRDef,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
=> ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) ) ) ) ),
file('theBenchmark.p',mWCRDef) ).
fof(mTermin,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isTerminating0(W0)
<=> ! [W1,W2] :
( ( aElement0(W2)
& aElement0(W1) )
=> ( sdtmndtplgtdt0(W1,W0,W2)
=> iLess0(W2,W1) ) ) ) ),
file('theBenchmark.p',mTermin) ).
fof(mNFRDef,definition,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aNormalFormOfIn0(W2,W0,W1)
<=> ( ~ ? [W3] : aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) ) ) ),
file('theBenchmark.p',mNFRDef) ).
fof(mTermNF,axiom,
! [W0] :
( ( isTerminating0(W0)
& aRewritingSystem0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('theBenchmark.p',mTermNF) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('theBenchmark.p',m__656) ).
fof(m__656_01,hypothesis,
( isTerminating0(xR)
& ! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W0,xR,W1)
| ? [W2] :
( sdtmndtplgtdt0(W2,xR,W1)
& aReductOfIn0(W2,W0,xR)
& aElement0(W2) )
| aReductOfIn0(W1,W0,xR) )
=> iLess0(W1,W0) ) )
& isLocallyConfluent0(xR)
& ! [W0,W1,W2] :
( ( aReductOfIn0(W2,W0,xR)
& aReductOfIn0(W1,W0,xR)
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) ) ) ),
file('theBenchmark.p',m__656_01) ).
fof(m__731,hypothesis,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('theBenchmark.p',m__731) ).
fof(m__715,hypothesis,
! [W0,W1,W2] :
( ( ( sdtmndtasgtdt0(W0,xR,W2)
| sdtmndtplgtdt0(W0,xR,W2)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W2)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W2,W0,xR)
| W0 = W2 )
& ( sdtmndtasgtdt0(W0,xR,W1)
| sdtmndtplgtdt0(W0,xR,W1)
| ? [W3] :
( sdtmndtplgtdt0(W3,xR,W1)
& aReductOfIn0(W3,W0,xR)
& aElement0(W3) )
| aReductOfIn0(W1,W0,xR)
| W0 = W1 )
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( iLess0(W0,xa)
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) ) ) ),
file('theBenchmark.p',m__715) ).
fof(m__731_02,hypothesis,
( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xc)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) )
| aReductOfIn0(xc,xa,xR) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) )
| aReductOfIn0(xb,xa,xR) ) ),
file('theBenchmark.p',m__731_02) ).
fof(m__,conjecture,
? [W0] :
( ( sdtmndtasgtdt0(W0,xR,xb)
| sdtmndtplgtdt0(W0,xR,xb)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,xb)
& aReductOfIn0(W1,W0,xR)
& aElement0(W1) )
| aReductOfIn0(xb,W0,xR)
| W0 = xb )
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aElement0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aElement0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_0] :
( ~ aElement0(U_0)
| $true ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( ~ aElement0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
! [W0] :
( $true
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mRelSort]) ).
fof(f_2_2,plain,
! [U_1] :
( $true
| ~ aRewritingSystem0(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_1] : ~ aRewritingSystem0(U_1)
| $true ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
! [U_1] :
( ~ aRewritingSystem0(U_1)
| $true ),
inference(definitional_conversion,[status(esa)],[f_2_3]) ).
cnf(f_2_5,plain,
( ~ aRewritingSystem0(U_1)
| $true ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
! [W0,W1] :
( ! [W2] :
( aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mReduct]) ).
fof(f_3_2,plain,
! [U_4,U_3] :
( ! [U_2] :
( aElement0(U_2)
| ~ aReductOfIn0(U_2,U_4,U_3) )
| ~ aRewritingSystem0(U_3)
| ~ aElement0(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4,U_2,U_3] :
( aElement0(U_2)
| ~ aReductOfIn0(U_2,U_4,U_3)
| ~ aRewritingSystem0(U_3)
| ~ aElement0(U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( aElement0(U_2)
| ~ aReductOfIn0(U_2,U_4,U_3)
| ~ aRewritingSystem0(U_3)
| ~ aElement0(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [W0,W1] :
( $true
| ~ iLess0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mWFOrd]) ).
fof(f_4_2,plain,
! [U_6,U_5] :
( $true
| ~ iLess0(U_6,U_5)
| ~ aElement0(U_5)
| ~ aElement0(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_6,U_5] :
( $true
| ~ iLess0(U_6,U_5)
| ~ aElement0(U_5)
| ~ aElement0(U_6) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( $true
| ~ iLess0(U_6,U_5)
| ~ aElement0(U_5)
| ~ aElement0(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [W0,W1,W2] :
( $true
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCbr]) ).
fof(f_5_2,plain,
! [U_9,U_8,U_7] :
( $true
| ~ sdtmndtplgtdt0(U_9,U_8,U_7)
| ~ aElement0(U_7)
| ~ aRewritingSystem0(U_8)
| ~ aElement0(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8,U_7,U_9] :
( $true
| ~ sdtmndtplgtdt0(U_9,U_8,U_7)
| ~ aElement0(U_7)
| ~ aRewritingSystem0(U_8)
| ~ aElement0(U_9) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( $true
| ~ sdtmndtplgtdt0(U_9,U_8,U_7)
| ~ aElement0(U_7)
| ~ aRewritingSystem0(U_8)
| ~ aElement0(U_9) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [W0,W1,W2] :
( ( ( sdtmndtplgtdt0(W0,W1,W2)
| ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) ) )
& ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCDef]) ).
fof(f_6_2,plain,
! [U_14,U_13,U_12] :
( ( ( sdtmndtplgtdt0(U_14,U_13,U_12)
| ( ! [U_11] :
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11) )
& ~ aReductOfIn0(U_12,U_14,U_13) ) )
& ( ? [U_10] :
( sdtmndtplgtdt0(U_10,U_13,U_12)
& aReductOfIn0(U_10,U_14,U_13)
& aElement0(U_10) )
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12) ) )
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_14,U_13,U_12] :
( ( ( sdtmndtplgtdt0(U_14,U_13,U_12)
| ( ! [U_11] :
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11) )
& ~ aReductOfIn0(U_12,U_14,U_13) ) )
& ( ( sdtmndtplgtdt0(sK1(U_14,U_13,U_12),U_13,U_12)
& aReductOfIn0(sK1(U_14,U_13,U_12),U_14,U_13)
& aElement0(sK1(U_14,U_13,U_12)) )
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12) ) )
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_14,U_13,U_12))],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_14,U_11,U_12,U_13] :
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11)
| ~ sP1(U_14,U_11,U_12,U_13) )
& ! [U_14,U_11,U_12,U_13] :
( ~ aReductOfIn0(U_12,U_14,U_13)
| ~ sP1(U_14,U_11,U_12,U_13) )
& ! [U_14,U_12,U_13] :
( sdtmndtplgtdt0(sK1(U_14,U_13,U_12),U_13,U_12)
| ~ sP0(U_14,U_12,U_13) )
& ! [U_14,U_12,U_13] :
( aReductOfIn0(sK1(U_14,U_13,U_12),U_14,U_13)
| ~ sP0(U_14,U_12,U_13) )
& ! [U_14,U_12,U_13] :
( aElement0(sK1(U_14,U_13,U_12))
| ~ sP0(U_14,U_12,U_13) )
& ! [U_14,U_11,U_12,U_13] :
( sdtmndtplgtdt0(U_14,U_13,U_12)
| sP1(U_14,U_11,U_12,U_13)
| ~ sP2(U_14,U_11,U_12,U_13) )
& ! [U_14,U_11,U_12,U_13] :
( sP0(U_14,U_12,U_13)
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ sP2(U_14,U_11,U_12,U_13) )
& ! [U_14,U_11,U_12,U_13] :
( sP2(U_14,U_11,U_12,U_13)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_6_3]) ).
cnf(f_6_5,plain,
( sP2(U_14,U_11,U_12,U_13)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( sP0(U_14,U_12,U_13)
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ sP2(U_14,U_11,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( sdtmndtplgtdt0(U_14,U_13,U_12)
| sP1(U_14,U_11,U_12,U_13)
| ~ sP2(U_14,U_11,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_8,plain,
( aElement0(sK1(U_14,U_13,U_12))
| ~ sP0(U_14,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_9,plain,
( aReductOfIn0(sK1(U_14,U_13,U_12),U_14,U_13)
| ~ sP0(U_14,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_10,plain,
( sdtmndtplgtdt0(sK1(U_14,U_13,U_12),U_13,U_12)
| ~ sP0(U_14,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_11,plain,
( ~ aReductOfIn0(U_12,U_14,U_13)
| ~ sP1(U_14,U_11,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_12,plain,
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11)
| ~ sP1(U_14,U_11,U_12,U_13) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [W0,W1,W2,W3] :
( sdtmndtplgtdt0(W0,W1,W3)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCTrans]) ).
fof(f_7_2,plain,
! [U_18,U_17,U_16,U_15] :
( sdtmndtplgtdt0(U_18,U_17,U_15)
| ~ sdtmndtplgtdt0(U_16,U_17,U_15)
| ~ sdtmndtplgtdt0(U_18,U_17,U_16)
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aRewritingSystem0(U_17)
| ~ aElement0(U_18) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_18,U_16,U_17,U_15] :
( sdtmndtplgtdt0(U_18,U_17,U_15)
| ~ sdtmndtplgtdt0(U_16,U_17,U_15)
| ~ sdtmndtplgtdt0(U_18,U_17,U_16)
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aRewritingSystem0(U_17)
| ~ aElement0(U_18) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( sdtmndtplgtdt0(U_18,U_17,U_15)
| ~ sdtmndtplgtdt0(U_16,U_17,U_15)
| ~ sdtmndtplgtdt0(U_18,U_17,U_16)
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aRewritingSystem0(U_17)
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [W0,W1,W2] :
( ( ( sdtmndtasgtdt0(W0,W1,W2)
| ( ~ sdtmndtplgtdt0(W0,W1,W2)
& W0 != W2 ) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2
| ~ sdtmndtasgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCRDef]) ).
fof(f_8_2,plain,
! [U_21,U_20,U_19] :
( ( ( sdtmndtasgtdt0(U_21,U_20,U_19)
| ( ~ sdtmndtplgtdt0(U_21,U_20,U_19)
& U_21 != U_19 ) )
& ( sdtmndtplgtdt0(U_21,U_20,U_19)
| U_21 = U_19
| ~ sdtmndtasgtdt0(U_21,U_20,U_19) ) )
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_21,U_19,U_20] :
( ~ sdtmndtplgtdt0(U_21,U_20,U_19)
| ~ sP3(U_21,U_19,U_20) )
& ! [U_21,U_19,U_20] :
( U_21 != U_19
| ~ sP3(U_21,U_19,U_20) )
& ! [U_21,U_19,U_20] :
( sdtmndtasgtdt0(U_21,U_20,U_19)
| sP3(U_21,U_19,U_20)
| ~ sP4(U_21,U_19,U_20) )
& ! [U_21,U_19,U_20] :
( sdtmndtplgtdt0(U_21,U_20,U_19)
| U_21 = U_19
| ~ sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ sP4(U_21,U_19,U_20) )
& ! [U_21,U_19,U_20] :
( sP4(U_21,U_19,U_20)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP4(U_21,U_19,U_20)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( sdtmndtplgtdt0(U_21,U_20,U_19)
| U_21 = U_19
| ~ sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ sP4(U_21,U_19,U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( sdtmndtasgtdt0(U_21,U_20,U_19)
| sP3(U_21,U_19,U_20)
| ~ sP4(U_21,U_19,U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( U_21 != U_19
| ~ sP3(U_21,U_19,U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_8,plain,
( ~ sdtmndtplgtdt0(U_21,U_20,U_19)
| ~ sP3(U_21,U_19,U_20) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [W0,W1,W2,W3] :
( sdtmndtasgtdt0(W0,W1,W3)
| ~ sdtmndtasgtdt0(W2,W1,W3)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCRTrans]) ).
fof(f_9_2,plain,
! [U_25,U_24,U_23,U_22] :
( sdtmndtasgtdt0(U_25,U_24,U_22)
| ~ sdtmndtasgtdt0(U_23,U_24,U_22)
| ~ sdtmndtasgtdt0(U_25,U_24,U_23)
| ~ aElement0(U_22)
| ~ aElement0(U_23)
| ~ aRewritingSystem0(U_24)
| ~ aElement0(U_25) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_25,U_24,U_22,U_23] :
( sdtmndtasgtdt0(U_25,U_24,U_22)
| ~ sdtmndtasgtdt0(U_23,U_24,U_22)
| ~ sdtmndtasgtdt0(U_25,U_24,U_23)
| ~ aElement0(U_22)
| ~ aElement0(U_23)
| ~ aRewritingSystem0(U_24)
| ~ aElement0(U_25) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( sdtmndtasgtdt0(U_25,U_24,U_22)
| ~ sdtmndtasgtdt0(U_23,U_24,U_22)
| ~ sdtmndtasgtdt0(U_25,U_24,U_23)
| ~ aElement0(U_22)
| ~ aElement0(U_23)
| ~ aRewritingSystem0(U_24)
| ~ aElement0(U_25) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [W0] :
( ( ( isConfluent0(W0)
| ? [W1,W2,W3] :
( ! [W4] :
( ~ sdtmndtasgtdt0(W3,W0,W4)
| ~ sdtmndtasgtdt0(W2,W0,W4)
| ~ aElement0(W4) )
& sdtmndtasgtdt0(W1,W0,W3)
& sdtmndtasgtdt0(W1,W0,W2)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) ) )
& ( ! [W1,W2,W3] :
( ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) )
| ~ sdtmndtasgtdt0(W1,W0,W3)
| ~ sdtmndtasgtdt0(W1,W0,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) )
| ~ isConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mCRDef]) ).
fof(f_10_2,plain,
! [U_34] :
( ( ( isConfluent0(U_34)
| ? [U_33,U_32,U_31] :
( ! [U_30] :
( ~ sdtmndtasgtdt0(U_31,U_34,U_30)
| ~ sdtmndtasgtdt0(U_32,U_34,U_30)
| ~ aElement0(U_30) )
& sdtmndtasgtdt0(U_33,U_34,U_31)
& sdtmndtasgtdt0(U_33,U_34,U_32)
& aElement0(U_31)
& aElement0(U_32)
& aElement0(U_33) ) )
& ( ! [U_29,U_28,U_27] :
( ? [U_26] :
( sdtmndtasgtdt0(U_27,U_34,U_26)
& sdtmndtasgtdt0(U_28,U_34,U_26)
& aElement0(U_26) )
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29) )
| ~ isConfluent0(U_34) ) )
| ~ aRewritingSystem0(U_34) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_34] :
( ( ( isConfluent0(U_34)
| ? [U_33,U_32,U_31] :
( ! [U_30] :
( ~ sdtmndtasgtdt0(U_31,U_34,U_30)
| ~ sdtmndtasgtdt0(U_32,U_34,U_30)
| ~ aElement0(U_30) )
& sdtmndtasgtdt0(U_33,U_34,U_31)
& sdtmndtasgtdt0(U_33,U_34,U_32)
& aElement0(U_31)
& aElement0(U_32)
& aElement0(U_33) ) )
& ( ! [U_29,U_28,U_27] :
( ( sdtmndtasgtdt0(U_27,U_34,sK2(U_34,U_29,U_28,U_27))
& sdtmndtasgtdt0(U_28,U_34,sK2(U_34,U_29,U_28,U_27))
& aElement0(sK2(U_34,U_29,U_28,U_27)) )
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29) )
| ~ isConfluent0(U_34) ) )
| ~ aRewritingSystem0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_26,sK2(U_34,U_29,U_28,U_27))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_34] :
( ( ( isConfluent0(U_34)
| ? [U_32,U_31] :
( ! [U_30] :
( ~ sdtmndtasgtdt0(U_31,U_34,U_30)
| ~ sdtmndtasgtdt0(U_32,U_34,U_30)
| ~ aElement0(U_30) )
& sdtmndtasgtdt0(sK3(U_34),U_34,U_31)
& sdtmndtasgtdt0(sK3(U_34),U_34,U_32)
& aElement0(U_31)
& aElement0(U_32)
& aElement0(sK3(U_34)) ) )
& ( ! [U_29,U_28,U_27] :
( ( sdtmndtasgtdt0(U_27,U_34,sK2(U_34,U_29,U_28,U_27))
& sdtmndtasgtdt0(U_28,U_34,sK2(U_34,U_29,U_28,U_27))
& aElement0(sK2(U_34,U_29,U_28,U_27)) )
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29) )
| ~ isConfluent0(U_34) ) )
| ~ aRewritingSystem0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_33,sK3(U_34))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_34] :
( ( ( isConfluent0(U_34)
| ? [U_31] :
( ! [U_30] :
( ~ sdtmndtasgtdt0(U_31,U_34,U_30)
| ~ sdtmndtasgtdt0(sK4(U_34),U_34,U_30)
| ~ aElement0(U_30) )
& sdtmndtasgtdt0(sK3(U_34),U_34,U_31)
& sdtmndtasgtdt0(sK3(U_34),U_34,sK4(U_34))
& aElement0(U_31)
& aElement0(sK4(U_34))
& aElement0(sK3(U_34)) ) )
& ( ! [U_29,U_28,U_27] :
( ( sdtmndtasgtdt0(U_27,U_34,sK2(U_34,U_29,U_28,U_27))
& sdtmndtasgtdt0(U_28,U_34,sK2(U_34,U_29,U_28,U_27))
& aElement0(sK2(U_34,U_29,U_28,U_27)) )
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29) )
| ~ isConfluent0(U_34) ) )
| ~ aRewritingSystem0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_32,sK4(U_34))],[f_10_4]) ).
fof(f_10_6,plain,
! [U_34] :
( ( ( isConfluent0(U_34)
| ( ! [U_30] :
( ~ sdtmndtasgtdt0(sK5(U_34),U_34,U_30)
| ~ sdtmndtasgtdt0(sK4(U_34),U_34,U_30)
| ~ aElement0(U_30) )
& sdtmndtasgtdt0(sK3(U_34),U_34,sK5(U_34))
& sdtmndtasgtdt0(sK3(U_34),U_34,sK4(U_34))
& aElement0(sK5(U_34))
& aElement0(sK4(U_34))
& aElement0(sK3(U_34)) ) )
& ( ! [U_29,U_28,U_27] :
( ( sdtmndtasgtdt0(U_27,U_34,sK2(U_34,U_29,U_28,U_27))
& sdtmndtasgtdt0(U_28,U_34,sK2(U_34,U_29,U_28,U_27))
& aElement0(sK2(U_34,U_29,U_28,U_27)) )
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29) )
| ~ isConfluent0(U_34) ) )
| ~ aRewritingSystem0(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5(U_34))],[f_10_5]) ).
fof(f_10_7,plain,
( ! [U_30,U_34] :
( ~ sdtmndtasgtdt0(sK5(U_34),U_34,U_30)
| ~ sdtmndtasgtdt0(sK4(U_34),U_34,U_30)
| ~ aElement0(U_30)
| ~ sP6(U_30,U_34) )
& ! [U_30,U_34] :
( sdtmndtasgtdt0(sK3(U_34),U_34,sK5(U_34))
| ~ sP6(U_30,U_34) )
& ! [U_30,U_34] :
( sdtmndtasgtdt0(sK3(U_34),U_34,sK4(U_34))
| ~ sP6(U_30,U_34) )
& ! [U_30,U_34] :
( aElement0(sK5(U_34))
| ~ sP6(U_30,U_34) )
& ! [U_30,U_34] :
( aElement0(sK4(U_34))
| ~ sP6(U_30,U_34) )
& ! [U_30,U_34] :
( aElement0(sK3(U_34))
| ~ sP6(U_30,U_34) )
& ! [U_27,U_34,U_28,U_29] :
( sdtmndtasgtdt0(U_27,U_34,sK2(U_34,U_29,U_28,U_27))
| ~ sP5(U_27,U_34,U_28,U_29) )
& ! [U_27,U_34,U_28,U_29] :
( sdtmndtasgtdt0(U_28,U_34,sK2(U_34,U_29,U_28,U_27))
| ~ sP5(U_27,U_34,U_28,U_29) )
& ! [U_27,U_34,U_28,U_29] :
( aElement0(sK2(U_34,U_29,U_28,U_27))
| ~ sP5(U_27,U_34,U_28,U_29) )
& ! [U_30,U_27,U_34,U_28,U_29] :
( isConfluent0(U_34)
| sP6(U_30,U_34)
| ~ sP7(U_30,U_27,U_34,U_28,U_29) )
& ! [U_30,U_27,U_34,U_28,U_29] :
( sP5(U_27,U_34,U_28,U_29)
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29)
| ~ isConfluent0(U_34)
| ~ sP7(U_30,U_27,U_34,U_28,U_29) )
& ! [U_30,U_27,U_34,U_28,U_29] :
( sP7(U_30,U_27,U_34,U_28,U_29)
| ~ aRewritingSystem0(U_34) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6,sP7])],[f_10_6]) ).
cnf(f_10_8,plain,
( sP7(U_30,U_27,U_34,U_28,U_29)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_9,plain,
( sP5(U_27,U_34,U_28,U_29)
| ~ sdtmndtasgtdt0(U_29,U_34,U_27)
| ~ sdtmndtasgtdt0(U_29,U_34,U_28)
| ~ aElement0(U_27)
| ~ aElement0(U_28)
| ~ aElement0(U_29)
| ~ isConfluent0(U_34)
| ~ sP7(U_30,U_27,U_34,U_28,U_29) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_10,plain,
( isConfluent0(U_34)
| sP6(U_30,U_34)
| ~ sP7(U_30,U_27,U_34,U_28,U_29) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_11,plain,
( aElement0(sK2(U_34,U_29,U_28,U_27))
| ~ sP5(U_27,U_34,U_28,U_29) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_12,plain,
( sdtmndtasgtdt0(U_28,U_34,sK2(U_34,U_29,U_28,U_27))
| ~ sP5(U_27,U_34,U_28,U_29) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_13,plain,
( sdtmndtasgtdt0(U_27,U_34,sK2(U_34,U_29,U_28,U_27))
| ~ sP5(U_27,U_34,U_28,U_29) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_14,plain,
( aElement0(sK3(U_34))
| ~ sP6(U_30,U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_15,plain,
( aElement0(sK4(U_34))
| ~ sP6(U_30,U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_16,plain,
( aElement0(sK5(U_34))
| ~ sP6(U_30,U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_17,plain,
( sdtmndtasgtdt0(sK3(U_34),U_34,sK4(U_34))
| ~ sP6(U_30,U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_18,plain,
( sdtmndtasgtdt0(sK3(U_34),U_34,sK5(U_34))
| ~ sP6(U_30,U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
cnf(f_10_19,plain,
( ~ sdtmndtasgtdt0(sK5(U_34),U_34,U_30)
| ~ sdtmndtasgtdt0(sK4(U_34),U_34,U_30)
| ~ aElement0(U_30)
| ~ sP6(U_30,U_34) ),
inference(clausify,[status(thm)],[f_10_7]) ).
fof(f_11_1,plain,
! [W0] :
( ( ( isLocallyConfluent0(W0)
| ? [W1,W2,W3] :
( ! [W4] :
( ~ sdtmndtasgtdt0(W3,W0,W4)
| ~ sdtmndtasgtdt0(W2,W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) ) )
& ( ! [W1,W2,W3] :
( ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) )
| ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mWCRDef]) ).
fof(f_11_2,plain,
! [U_43] :
( ( ( isLocallyConfluent0(U_43)
| ? [U_42,U_41,U_40] :
( ! [U_39] :
( ~ sdtmndtasgtdt0(U_40,U_43,U_39)
| ~ sdtmndtasgtdt0(U_41,U_43,U_39)
| ~ aElement0(U_39) )
& aReductOfIn0(U_40,U_42,U_43)
& aReductOfIn0(U_41,U_42,U_43)
& aElement0(U_40)
& aElement0(U_41)
& aElement0(U_42) ) )
& ( ! [U_38,U_37,U_36] :
( ? [U_35] :
( sdtmndtasgtdt0(U_36,U_43,U_35)
& sdtmndtasgtdt0(U_37,U_43,U_35)
& aElement0(U_35) )
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38) )
| ~ isLocallyConfluent0(U_43) ) )
| ~ aRewritingSystem0(U_43) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_43] :
( ( ( isLocallyConfluent0(U_43)
| ? [U_42,U_41,U_40] :
( ! [U_39] :
( ~ sdtmndtasgtdt0(U_40,U_43,U_39)
| ~ sdtmndtasgtdt0(U_41,U_43,U_39)
| ~ aElement0(U_39) )
& aReductOfIn0(U_40,U_42,U_43)
& aReductOfIn0(U_41,U_42,U_43)
& aElement0(U_40)
& aElement0(U_41)
& aElement0(U_42) ) )
& ( ! [U_38,U_37,U_36] :
( ( sdtmndtasgtdt0(U_36,U_43,sK6(U_43,U_38,U_37,U_36))
& sdtmndtasgtdt0(U_37,U_43,sK6(U_43,U_38,U_37,U_36))
& aElement0(sK6(U_43,U_38,U_37,U_36)) )
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38) )
| ~ isLocallyConfluent0(U_43) ) )
| ~ aRewritingSystem0(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_35,sK6(U_43,U_38,U_37,U_36))],[f_11_2]) ).
fof(f_11_4,plain,
! [U_43] :
( ( ( isLocallyConfluent0(U_43)
| ? [U_41,U_40] :
( ! [U_39] :
( ~ sdtmndtasgtdt0(U_40,U_43,U_39)
| ~ sdtmndtasgtdt0(U_41,U_43,U_39)
| ~ aElement0(U_39) )
& aReductOfIn0(U_40,sK7(U_43),U_43)
& aReductOfIn0(U_41,sK7(U_43),U_43)
& aElement0(U_40)
& aElement0(U_41)
& aElement0(sK7(U_43)) ) )
& ( ! [U_38,U_37,U_36] :
( ( sdtmndtasgtdt0(U_36,U_43,sK6(U_43,U_38,U_37,U_36))
& sdtmndtasgtdt0(U_37,U_43,sK6(U_43,U_38,U_37,U_36))
& aElement0(sK6(U_43,U_38,U_37,U_36)) )
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38) )
| ~ isLocallyConfluent0(U_43) ) )
| ~ aRewritingSystem0(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_42,sK7(U_43))],[f_11_3]) ).
fof(f_11_5,plain,
! [U_43] :
( ( ( isLocallyConfluent0(U_43)
| ? [U_40] :
( ! [U_39] :
( ~ sdtmndtasgtdt0(U_40,U_43,U_39)
| ~ sdtmndtasgtdt0(sK8(U_43),U_43,U_39)
| ~ aElement0(U_39) )
& aReductOfIn0(U_40,sK7(U_43),U_43)
& aReductOfIn0(sK8(U_43),sK7(U_43),U_43)
& aElement0(U_40)
& aElement0(sK8(U_43))
& aElement0(sK7(U_43)) ) )
& ( ! [U_38,U_37,U_36] :
( ( sdtmndtasgtdt0(U_36,U_43,sK6(U_43,U_38,U_37,U_36))
& sdtmndtasgtdt0(U_37,U_43,sK6(U_43,U_38,U_37,U_36))
& aElement0(sK6(U_43,U_38,U_37,U_36)) )
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38) )
| ~ isLocallyConfluent0(U_43) ) )
| ~ aRewritingSystem0(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8(U_43))],[f_11_4]) ).
fof(f_11_6,plain,
! [U_43] :
( ( ( isLocallyConfluent0(U_43)
| ( ! [U_39] :
( ~ sdtmndtasgtdt0(sK9(U_43),U_43,U_39)
| ~ sdtmndtasgtdt0(sK8(U_43),U_43,U_39)
| ~ aElement0(U_39) )
& aReductOfIn0(sK9(U_43),sK7(U_43),U_43)
& aReductOfIn0(sK8(U_43),sK7(U_43),U_43)
& aElement0(sK9(U_43))
& aElement0(sK8(U_43))
& aElement0(sK7(U_43)) ) )
& ( ! [U_38,U_37,U_36] :
( ( sdtmndtasgtdt0(U_36,U_43,sK6(U_43,U_38,U_37,U_36))
& sdtmndtasgtdt0(U_37,U_43,sK6(U_43,U_38,U_37,U_36))
& aElement0(sK6(U_43,U_38,U_37,U_36)) )
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38) )
| ~ isLocallyConfluent0(U_43) ) )
| ~ aRewritingSystem0(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_40,sK9(U_43))],[f_11_5]) ).
fof(f_11_7,plain,
( ! [U_43,U_39] :
( ~ sdtmndtasgtdt0(sK9(U_43),U_43,U_39)
| ~ sdtmndtasgtdt0(sK8(U_43),U_43,U_39)
| ~ aElement0(U_39)
| ~ sP9(U_43,U_39) )
& ! [U_43,U_39] :
( aReductOfIn0(sK9(U_43),sK7(U_43),U_43)
| ~ sP9(U_43,U_39) )
& ! [U_43,U_39] :
( aReductOfIn0(sK8(U_43),sK7(U_43),U_43)
| ~ sP9(U_43,U_39) )
& ! [U_43,U_39] :
( aElement0(sK9(U_43))
| ~ sP9(U_43,U_39) )
& ! [U_43,U_39] :
( aElement0(sK8(U_43))
| ~ sP9(U_43,U_39) )
& ! [U_43,U_39] :
( aElement0(sK7(U_43))
| ~ sP9(U_43,U_39) )
& ! [U_43,U_38,U_37,U_36] :
( sdtmndtasgtdt0(U_36,U_43,sK6(U_43,U_38,U_37,U_36))
| ~ sP8(U_43,U_38,U_37,U_36) )
& ! [U_43,U_38,U_37,U_36] :
( sdtmndtasgtdt0(U_37,U_43,sK6(U_43,U_38,U_37,U_36))
| ~ sP8(U_43,U_38,U_37,U_36) )
& ! [U_43,U_38,U_37,U_36] :
( aElement0(sK6(U_43,U_38,U_37,U_36))
| ~ sP8(U_43,U_38,U_37,U_36) )
& ! [U_43,U_38,U_39,U_37,U_36] :
( isLocallyConfluent0(U_43)
| sP9(U_43,U_39)
| ~ sP10(U_43,U_38,U_39,U_37,U_36) )
& ! [U_43,U_38,U_39,U_37,U_36] :
( sP8(U_43,U_38,U_37,U_36)
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38)
| ~ isLocallyConfluent0(U_43)
| ~ sP10(U_43,U_38,U_39,U_37,U_36) )
& ! [U_43,U_38,U_39,U_37,U_36] :
( sP10(U_43,U_38,U_39,U_37,U_36)
| ~ aRewritingSystem0(U_43) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9,sP10])],[f_11_6]) ).
cnf(f_11_8,plain,
( sP10(U_43,U_38,U_39,U_37,U_36)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_9,plain,
( sP8(U_43,U_38,U_37,U_36)
| ~ aReductOfIn0(U_36,U_38,U_43)
| ~ aReductOfIn0(U_37,U_38,U_43)
| ~ aElement0(U_36)
| ~ aElement0(U_37)
| ~ aElement0(U_38)
| ~ isLocallyConfluent0(U_43)
| ~ sP10(U_43,U_38,U_39,U_37,U_36) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_10,plain,
( isLocallyConfluent0(U_43)
| sP9(U_43,U_39)
| ~ sP10(U_43,U_38,U_39,U_37,U_36) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_11,plain,
( aElement0(sK6(U_43,U_38,U_37,U_36))
| ~ sP8(U_43,U_38,U_37,U_36) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_12,plain,
( sdtmndtasgtdt0(U_37,U_43,sK6(U_43,U_38,U_37,U_36))
| ~ sP8(U_43,U_38,U_37,U_36) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_13,plain,
( sdtmndtasgtdt0(U_36,U_43,sK6(U_43,U_38,U_37,U_36))
| ~ sP8(U_43,U_38,U_37,U_36) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_14,plain,
( aElement0(sK7(U_43))
| ~ sP9(U_43,U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_15,plain,
( aElement0(sK8(U_43))
| ~ sP9(U_43,U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_16,plain,
( aElement0(sK9(U_43))
| ~ sP9(U_43,U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_17,plain,
( aReductOfIn0(sK8(U_43),sK7(U_43),U_43)
| ~ sP9(U_43,U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_18,plain,
( aReductOfIn0(sK9(U_43),sK7(U_43),U_43)
| ~ sP9(U_43,U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
cnf(f_11_19,plain,
( ~ sdtmndtasgtdt0(sK9(U_43),U_43,U_39)
| ~ sdtmndtasgtdt0(sK8(U_43),U_43,U_39)
| ~ aElement0(U_39)
| ~ sP9(U_43,U_39) ),
inference(clausify,[status(thm)],[f_11_7]) ).
fof(f_12_1,plain,
! [W0] :
( ( ( isTerminating0(W0)
| ? [W1,W2] :
( ~ iLess0(W2,W1)
& sdtmndtplgtdt0(W1,W0,W2)
& aElement0(W2)
& aElement0(W1) ) )
& ( ! [W1,W2] :
( iLess0(W2,W1)
| ~ sdtmndtplgtdt0(W1,W0,W2)
| ~ aElement0(W2)
| ~ aElement0(W1) )
| ~ isTerminating0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mTermin]) ).
fof(f_12_2,plain,
! [U_48] :
( ( ( isTerminating0(U_48)
| ? [U_47,U_46] :
( ~ iLess0(U_46,U_47)
& sdtmndtplgtdt0(U_47,U_48,U_46)
& aElement0(U_46)
& aElement0(U_47) ) )
& ( ! [U_45,U_44] :
( iLess0(U_44,U_45)
| ~ sdtmndtplgtdt0(U_45,U_48,U_44)
| ~ aElement0(U_44)
| ~ aElement0(U_45) )
| ~ isTerminating0(U_48) ) )
| ~ aRewritingSystem0(U_48) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_48] :
( ( ( isTerminating0(U_48)
| ? [U_46] :
( ~ iLess0(U_46,sK10(U_48))
& sdtmndtplgtdt0(sK10(U_48),U_48,U_46)
& aElement0(U_46)
& aElement0(sK10(U_48)) ) )
& ( ! [U_45,U_44] :
( iLess0(U_44,U_45)
| ~ sdtmndtplgtdt0(U_45,U_48,U_44)
| ~ aElement0(U_44)
| ~ aElement0(U_45) )
| ~ isTerminating0(U_48) ) )
| ~ aRewritingSystem0(U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_47,sK10(U_48))],[f_12_2]) ).
fof(f_12_4,plain,
! [U_48] :
( ( ( isTerminating0(U_48)
| ( ~ iLess0(sK11(U_48),sK10(U_48))
& sdtmndtplgtdt0(sK10(U_48),U_48,sK11(U_48))
& aElement0(sK11(U_48))
& aElement0(sK10(U_48)) ) )
& ( ! [U_45,U_44] :
( iLess0(U_44,U_45)
| ~ sdtmndtplgtdt0(U_45,U_48,U_44)
| ~ aElement0(U_44)
| ~ aElement0(U_45) )
| ~ isTerminating0(U_48) ) )
| ~ aRewritingSystem0(U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_46,sK11(U_48))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_48] :
( ~ iLess0(sK11(U_48),sK10(U_48))
| ~ sP11(U_48) )
& ! [U_48] :
( sdtmndtplgtdt0(sK10(U_48),U_48,sK11(U_48))
| ~ sP11(U_48) )
& ! [U_48] :
( aElement0(sK11(U_48))
| ~ sP11(U_48) )
& ! [U_48] :
( aElement0(sK10(U_48))
| ~ sP11(U_48) )
& ! [U_45,U_44,U_48] :
( isTerminating0(U_48)
| sP11(U_48)
| ~ sP12(U_45,U_44,U_48) )
& ! [U_45,U_44,U_48] :
( iLess0(U_44,U_45)
| ~ sdtmndtplgtdt0(U_45,U_48,U_44)
| ~ aElement0(U_44)
| ~ aElement0(U_45)
| ~ isTerminating0(U_48)
| ~ sP12(U_45,U_44,U_48) )
& ! [U_45,U_44,U_48] :
( sP12(U_45,U_44,U_48)
| ~ aRewritingSystem0(U_48) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11,sP12])],[f_12_4]) ).
cnf(f_12_6,plain,
( sP12(U_45,U_44,U_48)
| ~ aRewritingSystem0(U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( iLess0(U_44,U_45)
| ~ sdtmndtplgtdt0(U_45,U_48,U_44)
| ~ aElement0(U_44)
| ~ aElement0(U_45)
| ~ isTerminating0(U_48)
| ~ sP12(U_45,U_44,U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( isTerminating0(U_48)
| sP11(U_48)
| ~ sP12(U_45,U_44,U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( aElement0(sK10(U_48))
| ~ sP11(U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_10,plain,
( aElement0(sK11(U_48))
| ~ sP11(U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_11,plain,
( sdtmndtplgtdt0(sK10(U_48),U_48,sK11(U_48))
| ~ sP11(U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_12,plain,
( ~ iLess0(sK11(U_48),sK10(U_48))
| ~ sP11(U_48) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
! [W0,W1] :
( ! [W2] :
( ( aNormalFormOfIn0(W2,W0,W1)
| ? [W3] : aReductOfIn0(W3,W2,W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W2) )
& ( ( ! [W3] : ~ aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) )
| ~ aNormalFormOfIn0(W2,W0,W1) ) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mNFRDef]) ).
fof(f_13_2,plain,
! [U_53,U_52] :
( ! [U_51] :
( ( aNormalFormOfIn0(U_51,U_53,U_52)
| ? [U_50] : aReductOfIn0(U_50,U_51,U_52)
| ~ sdtmndtasgtdt0(U_53,U_52,U_51)
| ~ aElement0(U_51) )
& ( ( ! [U_49] : ~ aReductOfIn0(U_49,U_51,U_52)
& sdtmndtasgtdt0(U_53,U_52,U_51)
& aElement0(U_51) )
| ~ aNormalFormOfIn0(U_51,U_53,U_52) ) )
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_53,U_52] :
( ( ! [U_55] :
( aNormalFormOfIn0(U_55,U_53,U_52)
| ? [U_50] : aReductOfIn0(U_50,U_55,U_52)
| ~ sdtmndtasgtdt0(U_53,U_52,U_55)
| ~ aElement0(U_55) )
& ! [U_54] :
( ( ! [U_49] : ~ aReductOfIn0(U_49,U_54,U_52)
& sdtmndtasgtdt0(U_53,U_52,U_54)
& aElement0(U_54) )
| ~ aNormalFormOfIn0(U_54,U_53,U_52) ) )
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_53,U_52] :
( ( ! [U_55] :
( aNormalFormOfIn0(U_55,U_53,U_52)
| aReductOfIn0(sK12(U_53,U_52,U_55),U_55,U_52)
| ~ sdtmndtasgtdt0(U_53,U_52,U_55)
| ~ aElement0(U_55) )
& ! [U_54] :
( ( ! [U_49] : ~ aReductOfIn0(U_49,U_54,U_52)
& sdtmndtasgtdt0(U_53,U_52,U_54)
& aElement0(U_54) )
| ~ aNormalFormOfIn0(U_54,U_53,U_52) ) )
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_50,sK12(U_53,U_52,U_55))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_53,U_49,U_54,U_52] :
( ~ aReductOfIn0(U_49,U_54,U_52)
| ~ sP13(U_53,U_49,U_54,U_52) )
& ! [U_53,U_49,U_54,U_52] :
( sdtmndtasgtdt0(U_53,U_52,U_54)
| ~ sP13(U_53,U_49,U_54,U_52) )
& ! [U_53,U_49,U_54,U_52] :
( aElement0(U_54)
| ~ sP13(U_53,U_49,U_54,U_52) )
& ! [U_55,U_53,U_49,U_54,U_52] :
( aNormalFormOfIn0(U_55,U_53,U_52)
| aReductOfIn0(sK12(U_53,U_52,U_55),U_55,U_52)
| ~ sdtmndtasgtdt0(U_53,U_52,U_55)
| ~ aElement0(U_55)
| ~ sP14(U_55,U_53,U_49,U_54,U_52) )
& ! [U_55,U_53,U_49,U_54,U_52] :
( sP13(U_53,U_49,U_54,U_52)
| ~ aNormalFormOfIn0(U_54,U_53,U_52)
| ~ sP14(U_55,U_53,U_49,U_54,U_52) )
& ! [U_55,U_53,U_49,U_54,U_52] :
( sP14(U_55,U_53,U_49,U_54,U_52)
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13,sP14])],[f_13_4]) ).
cnf(f_13_6,plain,
( sP14(U_55,U_53,U_49,U_54,U_52)
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( sP13(U_53,U_49,U_54,U_52)
| ~ aNormalFormOfIn0(U_54,U_53,U_52)
| ~ sP14(U_55,U_53,U_49,U_54,U_52) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_8,plain,
( aNormalFormOfIn0(U_55,U_53,U_52)
| aReductOfIn0(sK12(U_53,U_52,U_55),U_55,U_52)
| ~ sdtmndtasgtdt0(U_53,U_52,U_55)
| ~ aElement0(U_55)
| ~ sP14(U_55,U_53,U_49,U_54,U_52) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_9,plain,
( aElement0(U_54)
| ~ sP13(U_53,U_49,U_54,U_52) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_10,plain,
( sdtmndtasgtdt0(U_53,U_52,U_54)
| ~ sP13(U_53,U_49,U_54,U_52) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_11,plain,
( ~ aReductOfIn0(U_49,U_54,U_52)
| ~ sP13(U_53,U_49,U_54,U_52) ),
inference(clausify,[status(thm)],[f_13_5]) ).
fof(f_14_1,plain,
! [W0] :
( ! [W1] :
( ? [W2] : aNormalFormOfIn0(W2,W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mTermNF]) ).
fof(f_14_2,plain,
! [U_58] :
( ! [U_57] :
( ? [U_56] : aNormalFormOfIn0(U_56,U_57,U_58)
| ~ aElement0(U_57) )
| ~ isTerminating0(U_58)
| ~ aRewritingSystem0(U_58) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_58] :
( ! [U_57] :
( aNormalFormOfIn0(sK13(U_58,U_57),U_57,U_58)
| ~ aElement0(U_57) )
| ~ isTerminating0(U_58)
| ~ aRewritingSystem0(U_58) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_56,sK13(U_58,U_57))],[f_14_2]) ).
fof(f_14_4,plain,
! [U_58,U_57] :
( aNormalFormOfIn0(sK13(U_58,U_57),U_57,U_58)
| ~ aElement0(U_57)
| ~ isTerminating0(U_58)
| ~ aRewritingSystem0(U_58) ),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
( aNormalFormOfIn0(sK13(U_58,U_57),U_57,U_58)
| ~ aElement0(U_57)
| ~ isTerminating0(U_58)
| ~ aRewritingSystem0(U_58) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
aRewritingSystem0(xR),
inference(fof_nnf,[status(thm)],[m__656]) ).
fof(f_15_2,plain,
aRewritingSystem0(xR),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
( isTerminating0(xR)
& ! [W0,W1] :
( iLess0(W1,W0)
| ( ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ sdtmndtplgtdt0(W2,xR,W1)
| ~ aReductOfIn0(W2,W0,xR)
| ~ aElement0(W2) )
& ~ aReductOfIn0(W1,W0,xR) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
& isLocallyConfluent0(xR)
& ! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) )
| ~ aReductOfIn0(W2,W0,xR)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(fof_nnf,[status(thm)],[m__656_01]) ).
fof(f_16_2,plain,
( isTerminating0(xR)
& ! [U_67,U_66] :
( iLess0(U_66,U_67)
| ( ~ sdtmndtplgtdt0(U_67,xR,U_66)
& ! [U_65] :
( ~ sdtmndtplgtdt0(U_65,xR,U_66)
| ~ aReductOfIn0(U_65,U_67,xR)
| ~ aElement0(U_65) )
& ~ aReductOfIn0(U_66,U_67,xR) )
| ~ aElement0(U_66)
| ~ aElement0(U_67) )
& isLocallyConfluent0(xR)
& ! [U_64,U_63,U_62] :
( ? [U_61] :
( sdtmndtasgtdt0(U_62,xR,U_61)
& ( ( sdtmndtplgtdt0(U_62,xR,U_61)
& ( ? [U_60] :
( sdtmndtplgtdt0(U_60,xR,U_61)
& aReductOfIn0(U_60,U_62,xR)
& aElement0(U_60) )
| aReductOfIn0(U_61,U_62,xR) ) )
| U_62 = U_61 )
& sdtmndtasgtdt0(U_63,xR,U_61)
& ( ( sdtmndtplgtdt0(U_63,xR,U_61)
& ( ? [U_59] :
( sdtmndtplgtdt0(U_59,xR,U_61)
& aReductOfIn0(U_59,U_63,xR)
& aElement0(U_59) )
| aReductOfIn0(U_61,U_63,xR) ) )
| U_63 = U_61 )
& aElement0(U_61) )
| ~ aReductOfIn0(U_62,U_64,xR)
| ~ aReductOfIn0(U_63,U_64,xR)
| ~ aElement0(U_62)
| ~ aElement0(U_63)
| ~ aElement0(U_64) ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( isTerminating0(xR)
& ! [U_67,U_66] :
( iLess0(U_66,U_67)
| ( ~ sdtmndtplgtdt0(U_67,xR,U_66)
& ! [U_65] :
( ~ sdtmndtplgtdt0(U_65,xR,U_66)
| ~ aReductOfIn0(U_65,U_67,xR)
| ~ aElement0(U_65) )
& ~ aReductOfIn0(U_66,U_67,xR) )
| ~ aElement0(U_66)
| ~ aElement0(U_67) )
& isLocallyConfluent0(xR)
& ! [U_64,U_63,U_62] :
( ( sdtmndtasgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
& ( ? [U_60] :
( sdtmndtplgtdt0(U_60,xR,sK14(U_64,U_63,U_62))
& aReductOfIn0(U_60,U_62,xR)
& aElement0(U_60) )
| aReductOfIn0(sK14(U_64,U_63,U_62),U_62,xR) ) )
| U_62 = sK14(U_64,U_63,U_62) )
& sdtmndtasgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
& ( ? [U_59] :
( sdtmndtplgtdt0(U_59,xR,sK14(U_64,U_63,U_62))
& aReductOfIn0(U_59,U_63,xR)
& aElement0(U_59) )
| aReductOfIn0(sK14(U_64,U_63,U_62),U_63,xR) ) )
| U_63 = sK14(U_64,U_63,U_62) )
& aElement0(sK14(U_64,U_63,U_62)) )
| ~ aReductOfIn0(U_62,U_64,xR)
| ~ aReductOfIn0(U_63,U_64,xR)
| ~ aElement0(U_62)
| ~ aElement0(U_63)
| ~ aElement0(U_64) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_61,sK14(U_64,U_63,U_62))],[f_16_2]) ).
fof(f_16_4,plain,
( isTerminating0(xR)
& ! [U_67,U_66] :
( iLess0(U_66,U_67)
| ( ~ sdtmndtplgtdt0(U_67,xR,U_66)
& ! [U_65] :
( ~ sdtmndtplgtdt0(U_65,xR,U_66)
| ~ aReductOfIn0(U_65,U_67,xR)
| ~ aElement0(U_65) )
& ~ aReductOfIn0(U_66,U_67,xR) )
| ~ aElement0(U_66)
| ~ aElement0(U_67) )
& isLocallyConfluent0(xR)
& ! [U_64,U_63,U_62] :
( ( sdtmndtasgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
& ( ? [U_60] :
( sdtmndtplgtdt0(U_60,xR,sK14(U_64,U_63,U_62))
& aReductOfIn0(U_60,U_62,xR)
& aElement0(U_60) )
| aReductOfIn0(sK14(U_64,U_63,U_62),U_62,xR) ) )
| U_62 = sK14(U_64,U_63,U_62) )
& sdtmndtasgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(sK15(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
& aReductOfIn0(sK15(U_64,U_63,U_62),U_63,xR)
& aElement0(sK15(U_64,U_63,U_62)) )
| aReductOfIn0(sK14(U_64,U_63,U_62),U_63,xR) ) )
| U_63 = sK14(U_64,U_63,U_62) )
& aElement0(sK14(U_64,U_63,U_62)) )
| ~ aReductOfIn0(U_62,U_64,xR)
| ~ aReductOfIn0(U_63,U_64,xR)
| ~ aElement0(U_62)
| ~ aElement0(U_63)
| ~ aElement0(U_64) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_59,sK15(U_64,U_63,U_62))],[f_16_3]) ).
fof(f_16_5,plain,
( isTerminating0(xR)
& ! [U_67,U_66] :
( iLess0(U_66,U_67)
| ( ~ sdtmndtplgtdt0(U_67,xR,U_66)
& ! [U_65] :
( ~ sdtmndtplgtdt0(U_65,xR,U_66)
| ~ aReductOfIn0(U_65,U_67,xR)
| ~ aElement0(U_65) )
& ~ aReductOfIn0(U_66,U_67,xR) )
| ~ aElement0(U_66)
| ~ aElement0(U_67) )
& isLocallyConfluent0(xR)
& ! [U_64,U_63,U_62] :
( ( sdtmndtasgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(sK16(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
& aReductOfIn0(sK16(U_64,U_63,U_62),U_62,xR)
& aElement0(sK16(U_64,U_63,U_62)) )
| aReductOfIn0(sK14(U_64,U_63,U_62),U_62,xR) ) )
| U_62 = sK14(U_64,U_63,U_62) )
& sdtmndtasgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
& ( ( sdtmndtplgtdt0(sK15(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
& aReductOfIn0(sK15(U_64,U_63,U_62),U_63,xR)
& aElement0(sK15(U_64,U_63,U_62)) )
| aReductOfIn0(sK14(U_64,U_63,U_62),U_63,xR) ) )
| U_63 = sK14(U_64,U_63,U_62) )
& aElement0(sK14(U_64,U_63,U_62)) )
| ~ aReductOfIn0(U_62,U_64,xR)
| ~ aReductOfIn0(U_63,U_64,xR)
| ~ aElement0(U_62)
| ~ aElement0(U_63)
| ~ aElement0(U_64) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_60,sK16(U_64,U_63,U_62))],[f_16_4]) ).
fof(f_16_6,plain,
( ! [U_65,U_66,U_67] :
( ~ sdtmndtplgtdt0(U_67,xR,U_66)
| ~ sP20(U_65,U_66,U_67) )
& ! [U_65,U_66,U_67] :
( ~ sdtmndtplgtdt0(U_65,xR,U_66)
| ~ aReductOfIn0(U_65,U_67,xR)
| ~ aElement0(U_65)
| ~ sP20(U_65,U_66,U_67) )
& ! [U_65,U_66,U_67] :
( ~ aReductOfIn0(U_66,U_67,xR)
| ~ sP20(U_65,U_66,U_67) )
& ! [U_64,U_62,U_63] :
( sdtmndtplgtdt0(sK16(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
| ~ sP17(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( aReductOfIn0(sK16(U_64,U_63,U_62),U_62,xR)
| ~ sP17(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( aElement0(sK16(U_64,U_63,U_62))
| ~ sP17(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sdtmndtplgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
| ~ sP18(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sP17(U_64,U_62,U_63)
| aReductOfIn0(sK14(U_64,U_63,U_62),U_62,xR)
| ~ sP18(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sdtmndtplgtdt0(sK15(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
| ~ sP15(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( aReductOfIn0(sK15(U_64,U_63,U_62),U_63,xR)
| ~ sP15(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( aElement0(sK15(U_64,U_63,U_62))
| ~ sP15(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sdtmndtplgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
| ~ sP16(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sP15(U_64,U_62,U_63)
| aReductOfIn0(sK14(U_64,U_63,U_62),U_63,xR)
| ~ sP16(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sdtmndtasgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
| ~ sP19(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sP18(U_64,U_62,U_63)
| U_62 = sK14(U_64,U_63,U_62)
| ~ sP19(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sdtmndtasgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
| ~ sP19(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( sP16(U_64,U_62,U_63)
| U_63 = sK14(U_64,U_63,U_62)
| ~ sP19(U_64,U_62,U_63) )
& ! [U_64,U_62,U_63] :
( aElement0(sK14(U_64,U_63,U_62))
| ~ sP19(U_64,U_62,U_63) )
& isTerminating0(xR)
& ! [U_65,U_66,U_67] :
( iLess0(U_66,U_67)
| sP20(U_65,U_66,U_67)
| ~ aElement0(U_66)
| ~ aElement0(U_67) )
& isLocallyConfluent0(xR)
& ! [U_64,U_62,U_63] :
( sP19(U_64,U_62,U_63)
| ~ aReductOfIn0(U_62,U_64,xR)
| ~ aReductOfIn0(U_63,U_64,xR)
| ~ aElement0(U_62)
| ~ aElement0(U_63)
| ~ aElement0(U_64) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15,sP16,sP17,sP18,sP19,sP20])],[f_16_5]) ).
cnf(f_16_7,plain,
( sP19(U_64,U_62,U_63)
| ~ aReductOfIn0(U_62,U_64,xR)
| ~ aReductOfIn0(U_63,U_64,xR)
| ~ aElement0(U_62)
| ~ aElement0(U_63)
| ~ aElement0(U_64) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_8,plain,
isLocallyConfluent0(xR),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_9,plain,
( iLess0(U_66,U_67)
| sP20(U_65,U_66,U_67)
| ~ aElement0(U_66)
| ~ aElement0(U_67) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_10,plain,
isTerminating0(xR),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_11,plain,
( aElement0(sK14(U_64,U_63,U_62))
| ~ sP19(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_12,plain,
( sP16(U_64,U_62,U_63)
| U_63 = sK14(U_64,U_63,U_62)
| ~ sP19(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_13,plain,
( sdtmndtasgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
| ~ sP19(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_14,plain,
( sP18(U_64,U_62,U_63)
| U_62 = sK14(U_64,U_63,U_62)
| ~ sP19(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_15,plain,
( sdtmndtasgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
| ~ sP19(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_16,plain,
( sP15(U_64,U_62,U_63)
| aReductOfIn0(sK14(U_64,U_63,U_62),U_63,xR)
| ~ sP16(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_17,plain,
( sdtmndtplgtdt0(U_63,xR,sK14(U_64,U_63,U_62))
| ~ sP16(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_18,plain,
( aElement0(sK15(U_64,U_63,U_62))
| ~ sP15(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_19,plain,
( aReductOfIn0(sK15(U_64,U_63,U_62),U_63,xR)
| ~ sP15(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_20,plain,
( sdtmndtplgtdt0(sK15(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
| ~ sP15(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_21,plain,
( sP17(U_64,U_62,U_63)
| aReductOfIn0(sK14(U_64,U_63,U_62),U_62,xR)
| ~ sP18(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_22,plain,
( sdtmndtplgtdt0(U_62,xR,sK14(U_64,U_63,U_62))
| ~ sP18(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_23,plain,
( aElement0(sK16(U_64,U_63,U_62))
| ~ sP17(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_24,plain,
( aReductOfIn0(sK16(U_64,U_63,U_62),U_62,xR)
| ~ sP17(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_25,plain,
( sdtmndtplgtdt0(sK16(U_64,U_63,U_62),xR,sK14(U_64,U_63,U_62))
| ~ sP17(U_64,U_62,U_63) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_26,plain,
( ~ aReductOfIn0(U_66,U_67,xR)
| ~ sP20(U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_27,plain,
( ~ sdtmndtplgtdt0(U_65,xR,U_66)
| ~ aReductOfIn0(U_65,U_67,xR)
| ~ aElement0(U_65)
| ~ sP20(U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_16_6]) ).
cnf(f_16_28,plain,
( ~ sdtmndtplgtdt0(U_67,xR,U_66)
| ~ sP20(U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_16_6]) ).
fof(f_17_1,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(fof_nnf,[status(thm)],[m__731]) ).
fof(f_17_2,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
aElement0(xa),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
aElement0(xb),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_5,plain,
aElement0(xc),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& ( ( sdtmndtplgtdt0(W2,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W2,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W2,xR) ) )
| W2 = W3 )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( sdtmndtplgtdt0(W1,xR,W3)
& ( ? [W4] :
( sdtmndtplgtdt0(W4,xR,W3)
& aReductOfIn0(W4,W1,xR)
& aElement0(W4) )
| aReductOfIn0(W3,W1,xR) ) )
| W1 = W3 )
& aElement0(W3) )
| ~ iLess0(W0,xa)
| ( ~ sdtmndtasgtdt0(W0,xR,W2)
& ~ sdtmndtplgtdt0(W0,xR,W2)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W2)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,xR)
& W0 != W2 )
| ( ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W3] :
( ~ sdtmndtplgtdt0(W3,xR,W1)
| ~ aReductOfIn0(W3,W0,xR)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W1,W0,xR)
& W0 != W1 )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[m__715]) ).
fof(f_18_2,plain,
! [U_75,U_74,U_73] :
( ? [U_72] :
( sdtmndtasgtdt0(U_73,xR,U_72)
& ( ( sdtmndtplgtdt0(U_73,xR,U_72)
& ( ? [U_71] :
( sdtmndtplgtdt0(U_71,xR,U_72)
& aReductOfIn0(U_71,U_73,xR)
& aElement0(U_71) )
| aReductOfIn0(U_72,U_73,xR) ) )
| U_73 = U_72 )
& sdtmndtasgtdt0(U_74,xR,U_72)
& ( ( sdtmndtplgtdt0(U_74,xR,U_72)
& ( ? [U_70] :
( sdtmndtplgtdt0(U_70,xR,U_72)
& aReductOfIn0(U_70,U_74,xR)
& aElement0(U_70) )
| aReductOfIn0(U_72,U_74,xR) ) )
| U_74 = U_72 )
& aElement0(U_72) )
| ~ iLess0(U_75,xa)
| ( ~ sdtmndtasgtdt0(U_75,xR,U_73)
& ~ sdtmndtplgtdt0(U_75,xR,U_73)
& ! [U_69] :
( ~ sdtmndtplgtdt0(U_69,xR,U_73)
| ~ aReductOfIn0(U_69,U_75,xR)
| ~ aElement0(U_69) )
& ~ aReductOfIn0(U_73,U_75,xR)
& U_75 != U_73 )
| ( ~ sdtmndtasgtdt0(U_75,xR,U_74)
& ~ sdtmndtplgtdt0(U_75,xR,U_74)
& ! [U_68] :
( ~ sdtmndtplgtdt0(U_68,xR,U_74)
| ~ aReductOfIn0(U_68,U_75,xR)
| ~ aElement0(U_68) )
& ~ aReductOfIn0(U_74,U_75,xR)
& U_75 != U_74 )
| ~ aElement0(U_73)
| ~ aElement0(U_74)
| ~ aElement0(U_75) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_75,U_74,U_73] :
( ( sdtmndtasgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
& ( ? [U_71] :
( sdtmndtplgtdt0(U_71,xR,sK17(U_75,U_74,U_73))
& aReductOfIn0(U_71,U_73,xR)
& aElement0(U_71) )
| aReductOfIn0(sK17(U_75,U_74,U_73),U_73,xR) ) )
| U_73 = sK17(U_75,U_74,U_73) )
& sdtmndtasgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
& ( ? [U_70] :
( sdtmndtplgtdt0(U_70,xR,sK17(U_75,U_74,U_73))
& aReductOfIn0(U_70,U_74,xR)
& aElement0(U_70) )
| aReductOfIn0(sK17(U_75,U_74,U_73),U_74,xR) ) )
| U_74 = sK17(U_75,U_74,U_73) )
& aElement0(sK17(U_75,U_74,U_73)) )
| ~ iLess0(U_75,xa)
| ( ~ sdtmndtasgtdt0(U_75,xR,U_73)
& ~ sdtmndtplgtdt0(U_75,xR,U_73)
& ! [U_69] :
( ~ sdtmndtplgtdt0(U_69,xR,U_73)
| ~ aReductOfIn0(U_69,U_75,xR)
| ~ aElement0(U_69) )
& ~ aReductOfIn0(U_73,U_75,xR)
& U_75 != U_73 )
| ( ~ sdtmndtasgtdt0(U_75,xR,U_74)
& ~ sdtmndtplgtdt0(U_75,xR,U_74)
& ! [U_68] :
( ~ sdtmndtplgtdt0(U_68,xR,U_74)
| ~ aReductOfIn0(U_68,U_75,xR)
| ~ aElement0(U_68) )
& ~ aReductOfIn0(U_74,U_75,xR)
& U_75 != U_74 )
| ~ aElement0(U_73)
| ~ aElement0(U_74)
| ~ aElement0(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_72,sK17(U_75,U_74,U_73))],[f_18_2]) ).
fof(f_18_4,plain,
! [U_75,U_74,U_73] :
( ( sdtmndtasgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
& ( ? [U_71] :
( sdtmndtplgtdt0(U_71,xR,sK17(U_75,U_74,U_73))
& aReductOfIn0(U_71,U_73,xR)
& aElement0(U_71) )
| aReductOfIn0(sK17(U_75,U_74,U_73),U_73,xR) ) )
| U_73 = sK17(U_75,U_74,U_73) )
& sdtmndtasgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(sK18(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
& aReductOfIn0(sK18(U_75,U_74,U_73),U_74,xR)
& aElement0(sK18(U_75,U_74,U_73)) )
| aReductOfIn0(sK17(U_75,U_74,U_73),U_74,xR) ) )
| U_74 = sK17(U_75,U_74,U_73) )
& aElement0(sK17(U_75,U_74,U_73)) )
| ~ iLess0(U_75,xa)
| ( ~ sdtmndtasgtdt0(U_75,xR,U_73)
& ~ sdtmndtplgtdt0(U_75,xR,U_73)
& ! [U_69] :
( ~ sdtmndtplgtdt0(U_69,xR,U_73)
| ~ aReductOfIn0(U_69,U_75,xR)
| ~ aElement0(U_69) )
& ~ aReductOfIn0(U_73,U_75,xR)
& U_75 != U_73 )
| ( ~ sdtmndtasgtdt0(U_75,xR,U_74)
& ~ sdtmndtplgtdt0(U_75,xR,U_74)
& ! [U_68] :
( ~ sdtmndtplgtdt0(U_68,xR,U_74)
| ~ aReductOfIn0(U_68,U_75,xR)
| ~ aElement0(U_68) )
& ~ aReductOfIn0(U_74,U_75,xR)
& U_75 != U_74 )
| ~ aElement0(U_73)
| ~ aElement0(U_74)
| ~ aElement0(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_70,sK18(U_75,U_74,U_73))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_75,U_74,U_73] :
( ( sdtmndtasgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(sK19(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
& aReductOfIn0(sK19(U_75,U_74,U_73),U_73,xR)
& aElement0(sK19(U_75,U_74,U_73)) )
| aReductOfIn0(sK17(U_75,U_74,U_73),U_73,xR) ) )
| U_73 = sK17(U_75,U_74,U_73) )
& sdtmndtasgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
& ( ( sdtmndtplgtdt0(sK18(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
& aReductOfIn0(sK18(U_75,U_74,U_73),U_74,xR)
& aElement0(sK18(U_75,U_74,U_73)) )
| aReductOfIn0(sK17(U_75,U_74,U_73),U_74,xR) ) )
| U_74 = sK17(U_75,U_74,U_73) )
& aElement0(sK17(U_75,U_74,U_73)) )
| ~ iLess0(U_75,xa)
| ( ~ sdtmndtasgtdt0(U_75,xR,U_73)
& ~ sdtmndtplgtdt0(U_75,xR,U_73)
& ! [U_69] :
( ~ sdtmndtplgtdt0(U_69,xR,U_73)
| ~ aReductOfIn0(U_69,U_75,xR)
| ~ aElement0(U_69) )
& ~ aReductOfIn0(U_73,U_75,xR)
& U_75 != U_73 )
| ( ~ sdtmndtasgtdt0(U_75,xR,U_74)
& ~ sdtmndtplgtdt0(U_75,xR,U_74)
& ! [U_68] :
( ~ sdtmndtplgtdt0(U_68,xR,U_74)
| ~ aReductOfIn0(U_68,U_75,xR)
| ~ aElement0(U_68) )
& ~ aReductOfIn0(U_74,U_75,xR)
& U_75 != U_74 )
| ~ aElement0(U_73)
| ~ aElement0(U_74)
| ~ aElement0(U_75) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_71,sK19(U_75,U_74,U_73))],[f_18_4]) ).
fof(f_18_6,plain,
( ! [U_75,U_73,U_74] :
( sdtmndtplgtdt0(sK19(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
| ~ sP25(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( aReductOfIn0(sK19(U_75,U_74,U_73),U_73,xR)
| ~ sP25(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( aElement0(sK19(U_75,U_74,U_73))
| ~ sP25(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sdtmndtplgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
| ~ sP26(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sP25(U_75,U_73,U_74)
| aReductOfIn0(sK17(U_75,U_74,U_73),U_73,xR)
| ~ sP26(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sdtmndtplgtdt0(sK18(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
| ~ sP23(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( aReductOfIn0(sK18(U_75,U_74,U_73),U_74,xR)
| ~ sP23(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( aElement0(sK18(U_75,U_74,U_73))
| ~ sP23(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sdtmndtplgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
| ~ sP24(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sP23(U_75,U_73,U_74)
| aReductOfIn0(sK17(U_75,U_74,U_73),U_74,xR)
| ~ sP24(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sdtmndtasgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
| ~ sP27(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sP26(U_75,U_73,U_74)
| U_73 = sK17(U_75,U_74,U_73)
| ~ sP27(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sdtmndtasgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
| ~ sP27(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( sP24(U_75,U_73,U_74)
| U_74 = sK17(U_75,U_74,U_73)
| ~ sP27(U_75,U_73,U_74) )
& ! [U_75,U_73,U_74] :
( aElement0(sK17(U_75,U_74,U_73))
| ~ sP27(U_75,U_73,U_74) )
& ! [U_75,U_69,U_73] :
( ~ sdtmndtasgtdt0(U_75,xR,U_73)
| ~ sP22(U_75,U_69,U_73) )
& ! [U_75,U_69,U_73] :
( ~ sdtmndtplgtdt0(U_75,xR,U_73)
| ~ sP22(U_75,U_69,U_73) )
& ! [U_75,U_69,U_73] :
( ~ sdtmndtplgtdt0(U_69,xR,U_73)
| ~ aReductOfIn0(U_69,U_75,xR)
| ~ aElement0(U_69)
| ~ sP22(U_75,U_69,U_73) )
& ! [U_75,U_69,U_73] :
( ~ aReductOfIn0(U_73,U_75,xR)
| ~ sP22(U_75,U_69,U_73) )
& ! [U_75,U_69,U_73] :
( U_75 != U_73
| ~ sP22(U_75,U_69,U_73) )
& ! [U_75,U_74,U_68] :
( ~ sdtmndtasgtdt0(U_75,xR,U_74)
| ~ sP21(U_75,U_74,U_68) )
& ! [U_75,U_74,U_68] :
( ~ sdtmndtplgtdt0(U_75,xR,U_74)
| ~ sP21(U_75,U_74,U_68) )
& ! [U_75,U_74,U_68] :
( ~ sdtmndtplgtdt0(U_68,xR,U_74)
| ~ aReductOfIn0(U_68,U_75,xR)
| ~ aElement0(U_68)
| ~ sP21(U_75,U_74,U_68) )
& ! [U_75,U_74,U_68] :
( ~ aReductOfIn0(U_74,U_75,xR)
| ~ sP21(U_75,U_74,U_68) )
& ! [U_75,U_74,U_68] :
( U_75 != U_74
| ~ sP21(U_75,U_74,U_68) )
& ! [U_75,U_69,U_73,U_74,U_68] :
( sP27(U_75,U_73,U_74)
| ~ iLess0(U_75,xa)
| sP22(U_75,U_69,U_73)
| sP21(U_75,U_74,U_68)
| ~ aElement0(U_73)
| ~ aElement0(U_74)
| ~ aElement0(U_75) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22,sP23,sP24,sP25,sP26,sP27])],[f_18_5]) ).
cnf(f_18_7,plain,
( sP27(U_75,U_73,U_74)
| ~ iLess0(U_75,xa)
| sP22(U_75,U_69,U_73)
| sP21(U_75,U_74,U_68)
| ~ aElement0(U_73)
| ~ aElement0(U_74)
| ~ aElement0(U_75) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_8,plain,
( U_75 != U_74
| ~ sP21(U_75,U_74,U_68) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_9,plain,
( ~ aReductOfIn0(U_74,U_75,xR)
| ~ sP21(U_75,U_74,U_68) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_10,plain,
( ~ sdtmndtplgtdt0(U_68,xR,U_74)
| ~ aReductOfIn0(U_68,U_75,xR)
| ~ aElement0(U_68)
| ~ sP21(U_75,U_74,U_68) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_11,plain,
( ~ sdtmndtplgtdt0(U_75,xR,U_74)
| ~ sP21(U_75,U_74,U_68) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_12,plain,
( ~ sdtmndtasgtdt0(U_75,xR,U_74)
| ~ sP21(U_75,U_74,U_68) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_13,plain,
( U_75 != U_73
| ~ sP22(U_75,U_69,U_73) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_14,plain,
( ~ aReductOfIn0(U_73,U_75,xR)
| ~ sP22(U_75,U_69,U_73) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_15,plain,
( ~ sdtmndtplgtdt0(U_69,xR,U_73)
| ~ aReductOfIn0(U_69,U_75,xR)
| ~ aElement0(U_69)
| ~ sP22(U_75,U_69,U_73) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_16,plain,
( ~ sdtmndtplgtdt0(U_75,xR,U_73)
| ~ sP22(U_75,U_69,U_73) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_17,plain,
( ~ sdtmndtasgtdt0(U_75,xR,U_73)
| ~ sP22(U_75,U_69,U_73) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_18,plain,
( aElement0(sK17(U_75,U_74,U_73))
| ~ sP27(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_19,plain,
( sP24(U_75,U_73,U_74)
| U_74 = sK17(U_75,U_74,U_73)
| ~ sP27(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_20,plain,
( sdtmndtasgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
| ~ sP27(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_21,plain,
( sP26(U_75,U_73,U_74)
| U_73 = sK17(U_75,U_74,U_73)
| ~ sP27(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_22,plain,
( sdtmndtasgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
| ~ sP27(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_23,plain,
( sP23(U_75,U_73,U_74)
| aReductOfIn0(sK17(U_75,U_74,U_73),U_74,xR)
| ~ sP24(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_24,plain,
( sdtmndtplgtdt0(U_74,xR,sK17(U_75,U_74,U_73))
| ~ sP24(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_25,plain,
( aElement0(sK18(U_75,U_74,U_73))
| ~ sP23(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_26,plain,
( aReductOfIn0(sK18(U_75,U_74,U_73),U_74,xR)
| ~ sP23(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_27,plain,
( sdtmndtplgtdt0(sK18(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
| ~ sP23(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_28,plain,
( sP25(U_75,U_73,U_74)
| aReductOfIn0(sK17(U_75,U_74,U_73),U_73,xR)
| ~ sP26(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_29,plain,
( sdtmndtplgtdt0(U_73,xR,sK17(U_75,U_74,U_73))
| ~ sP26(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_30,plain,
( aElement0(sK19(U_75,U_74,U_73))
| ~ sP25(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_31,plain,
( aReductOfIn0(sK19(U_75,U_74,U_73),U_73,xR)
| ~ sP25(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
cnf(f_18_32,plain,
( sdtmndtplgtdt0(sK19(U_75,U_74,U_73),xR,sK17(U_75,U_74,U_73))
| ~ sP25(U_75,U_73,U_74) ),
inference(clausify,[status(thm)],[f_18_6]) ).
fof(f_19_1,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xc)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) )
| aReductOfIn0(xc,xa,xR) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) )
| aReductOfIn0(xb,xa,xR) ) ),
inference(fof_nnf,[status(thm)],[m__731_02]) ).
fof(f_19_2,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [U_77] :
( sdtmndtplgtdt0(U_77,xR,xc)
& aReductOfIn0(U_77,xa,xR)
& aElement0(U_77) )
| aReductOfIn0(xc,xa,xR) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( ? [U_76] :
( sdtmndtplgtdt0(U_76,xR,xb)
& aReductOfIn0(U_76,xa,xR)
& aElement0(U_76) )
| aReductOfIn0(xb,xa,xR) ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& ( ? [U_77] :
( sdtmndtplgtdt0(U_77,xR,xc)
& aReductOfIn0(U_77,xa,xR)
& aElement0(U_77) )
| aReductOfIn0(xc,xa,xR) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( ( sdtmndtplgtdt0(sK20,xR,xb)
& aReductOfIn0(sK20,xa,xR)
& aElement0(sK20) )
| aReductOfIn0(xb,xa,xR) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_76,sK20)],[f_19_2]) ).
fof(f_19_4,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& ( ( sdtmndtplgtdt0(sK21,xR,xc)
& aReductOfIn0(sK21,xa,xR)
& aElement0(sK21) )
| aReductOfIn0(xc,xa,xR) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( ( sdtmndtplgtdt0(sK20,xR,xb)
& aReductOfIn0(sK20,xa,xR)
& aElement0(sK20) )
| aReductOfIn0(xb,xa,xR) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_77,sK21)],[f_19_3]) ).
fof(f_19_5,plain,
( ( sdtmndtplgtdt0(sK21,xR,xc)
| ~ sP29 )
& ( aReductOfIn0(sK21,xa,xR)
| ~ sP29 )
& ( aElement0(sK21)
| ~ sP29 )
& ( sdtmndtplgtdt0(sK20,xR,xb)
| ~ sP28 )
& ( aReductOfIn0(sK20,xa,xR)
| ~ sP28 )
& ( aElement0(sK20)
| ~ sP28 )
& sdtmndtplgtdt0(xa,xR,xc)
& ( sP29
| aReductOfIn0(xc,xa,xR) )
& sdtmndtplgtdt0(xa,xR,xb)
& ( sP28
| aReductOfIn0(xb,xa,xR) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28,sP29])],[f_19_4]) ).
cnf(f_19_6,plain,
( sP28
| aReductOfIn0(xb,xa,xR) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_8,plain,
( sP29
| aReductOfIn0(xc,xa,xR) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_9,plain,
sdtmndtplgtdt0(xa,xR,xc),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_10,plain,
( aElement0(sK20)
| ~ sP28 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_11,plain,
( aReductOfIn0(sK20,xa,xR)
| ~ sP28 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_12,plain,
( sdtmndtplgtdt0(sK20,xR,xb)
| ~ sP28 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_13,plain,
( aElement0(sK21)
| ~ sP29 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_14,plain,
( aReductOfIn0(sK21,xa,xR)
| ~ sP29 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_15,plain,
( sdtmndtplgtdt0(sK21,xR,xc)
| ~ sP29 ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_1,negated_conjecture,
~ ? [W0] :
( ( sdtmndtasgtdt0(W0,xR,xb)
| sdtmndtplgtdt0(W0,xR,xb)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,xb)
& aReductOfIn0(W1,W0,xR)
& aElement0(W1) )
| aReductOfIn0(xb,W0,xR)
| W0 = xb )
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_20_2,negated_conjecture,
! [W0] :
( ( ~ sdtmndtasgtdt0(W0,xR,xb)
& ~ sdtmndtplgtdt0(W0,xR,xb)
& ! [W1] :
( ~ sdtmndtplgtdt0(W1,xR,xb)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(xb,W0,xR)
& W0 != xb )
| ~ aReductOfIn0(W0,xa,xR)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[f_20_1]) ).
fof(f_20_3,negated_conjecture,
! [U_79] :
( ( ~ sdtmndtasgtdt0(U_79,xR,xb)
& ~ sdtmndtplgtdt0(U_79,xR,xb)
& ! [U_78] :
( ~ sdtmndtplgtdt0(U_78,xR,xb)
| ~ aReductOfIn0(U_78,U_79,xR)
| ~ aElement0(U_78) )
& ~ aReductOfIn0(xb,U_79,xR)
& U_79 != xb )
| ~ aReductOfIn0(U_79,xa,xR)
| ~ aElement0(U_79) ),
inference(variable_rename,[status(thm)],[f_20_2]) ).
fof(f_20_4,negated_conjecture,
( ! [U_78,U_79] :
( ~ sdtmndtasgtdt0(U_79,xR,xb)
| ~ sP30(U_78,U_79) )
& ! [U_78,U_79] :
( ~ sdtmndtplgtdt0(U_79,xR,xb)
| ~ sP30(U_78,U_79) )
& ! [U_78,U_79] :
( ~ sdtmndtplgtdt0(U_78,xR,xb)
| ~ aReductOfIn0(U_78,U_79,xR)
| ~ aElement0(U_78)
| ~ sP30(U_78,U_79) )
& ! [U_78,U_79] :
( ~ aReductOfIn0(xb,U_79,xR)
| ~ sP30(U_78,U_79) )
& ! [U_78,U_79] :
( U_79 != xb
| ~ sP30(U_78,U_79) )
& ! [U_78,U_79] :
( sP30(U_78,U_79)
| ~ aReductOfIn0(U_79,xa,xR)
| ~ aElement0(U_79) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_20_3]) ).
cnf(f_20_5,negated_conjecture,
( sP30(U_78,U_79)
| ~ aReductOfIn0(U_79,xa,xR)
| ~ aElement0(U_79) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,negated_conjecture,
( U_79 != xb
| ~ sP30(U_78,U_79) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,negated_conjecture,
( ~ aReductOfIn0(xb,U_79,xR)
| ~ sP30(U_78,U_79) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_8,negated_conjecture,
( ~ sdtmndtplgtdt0(U_78,xR,xb)
| ~ aReductOfIn0(U_78,U_79,xR)
| ~ aElement0(U_78)
| ~ sP30(U_78,U_79) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_9,negated_conjecture,
( ~ sdtmndtplgtdt0(U_79,xR,xb)
| ~ sP30(U_78,U_79) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_10,negated_conjecture,
( ~ sdtmndtasgtdt0(U_79,xR,xb)
| ~ sP30(U_78,U_79) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_1_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_5]) ).
cnf(f_2_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_5]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_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,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( aRewritingSystem0(Eq_y_0)
| ~ aRewritingSystem0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( aReductOfIn0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ aReductOfIn0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( iLess0(Eq_y_0,Eq_y_1)
| ~ iLess0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sdtmndtplgtdt0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdtmndtplgtdt0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sdtmndtasgtdt0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdtmndtasgtdt0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( isConfluent0(Eq_y_0)
| ~ isConfluent0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( isLocallyConfluent0(Eq_y_0)
| ~ isLocallyConfluent0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( isTerminating0(Eq_y_0)
| ~ isTerminating0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( aNormalFormOfIn0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ aNormalFormOfIn0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP11(Eq_y_0)
| ~ sP11(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_50,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_51,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_52,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_53,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_55,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_56,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_57,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_58,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_59,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_60,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_61,axiom,
( sP30(Eq_y_0,Eq_y_1)
| ~ sP30(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM016+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n019.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 15:13:51 UTC 2026
% 0.18/0.45 % CPUTime :
% 30.70/31.11 % SZS status Theorem for theBenchmark
% 30.70/31.11 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------