%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM017+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 : n016.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 08:14:45 AM UTC 2026
% Result : Theorem 102.12s 102.49s
% Output : Proof 102.48s
% 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)
& isLocallyConfluent0(xR) ),
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)
& sdtmndtasgtdt0(W0,xR,W1)
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( iLess0(W0,xa)
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& sdtmndtasgtdt0(W1,xR,W3)
& aElement0(W3) ) ) ),
file('theBenchmark.p',m__715) ).
fof(m__731_02,hypothesis,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
file('theBenchmark.p',m__731_02) ).
fof(m__755,hypothesis,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('theBenchmark.p',m__755) ).
fof(m__779,hypothesis,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
file('theBenchmark.p',m__779) ).
fof(m__,conjecture,
? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& 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]) ).
cnf(f_1_4,plain,
( ~ aElement0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
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]) ).
cnf(f_2_4,plain,
( ~ aRewritingSystem0(U_1)
| $true ),
inference(clausify,[status(thm)],[f_2_3]) ).
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]) ).
cnf(f_3_3,plain,
( aElement0(U_2)
| ~ aReductOfIn0(U_2,U_4,U_3)
| ~ aRewritingSystem0(U_3)
| ~ aElement0(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
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]) ).
cnf(f_4_3,plain,
( $true
| ~ iLess0(U_6,U_5)
| ~ aElement0(U_5)
| ~ aElement0(U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
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]) ).
cnf(f_5_3,plain,
( $true
| ~ sdtmndtplgtdt0(U_9,U_8,U_7)
| ~ aElement0(U_7)
| ~ aRewritingSystem0(U_8)
| ~ aElement0(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
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]) ).
cnf(f_6_4,plain,
( 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(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( aReductOfIn0(sK1(U_14,U_13,U_12),U_14,U_13)
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( sdtmndtplgtdt0(sK1(U_14,U_13,U_12),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(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( ~ aReductOfIn0(U_12,U_14,U_13)
| sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11)
| sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
cnf(f_7_3,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_2]) ).
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]) ).
cnf(f_8_3,plain,
( 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(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_21 != U_19
| sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( ~ sdtmndtplgtdt0(U_21,U_20,U_19)
| sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_8_2]) ).
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]) ).
cnf(f_9_3,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_2]) ).
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]) ).
cnf(f_10_7,plain,
( 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(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_8,plain,
( sdtmndtasgtdt0(U_28,U_34,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(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_9,plain,
( sdtmndtasgtdt0(U_27,U_34,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(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_10,plain,
( aElement0(sK3(U_34))
| isConfluent0(U_34)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_11,plain,
( aElement0(sK4(U_34))
| isConfluent0(U_34)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_12,plain,
( aElement0(sK5(U_34))
| isConfluent0(U_34)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_13,plain,
( sdtmndtasgtdt0(sK3(U_34),U_34,sK4(U_34))
| isConfluent0(U_34)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_14,plain,
( sdtmndtasgtdt0(sK3(U_34),U_34,sK5(U_34))
| isConfluent0(U_34)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_15,plain,
( ~ sdtmndtasgtdt0(sK5(U_34),U_34,U_30)
| ~ sdtmndtasgtdt0(sK4(U_34),U_34,U_30)
| ~ aElement0(U_30)
| isConfluent0(U_34)
| ~ aRewritingSystem0(U_34) ),
inference(clausify,[status(thm)],[f_10_6]) ).
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]) ).
cnf(f_11_7,plain,
( 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(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_8,plain,
( sdtmndtasgtdt0(U_37,U_43,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(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_9,plain,
( sdtmndtasgtdt0(U_36,U_43,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(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_10,plain,
( aElement0(sK7(U_43))
| isLocallyConfluent0(U_43)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_11,plain,
( aElement0(sK8(U_43))
| isLocallyConfluent0(U_43)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_12,plain,
( aElement0(sK9(U_43))
| isLocallyConfluent0(U_43)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_13,plain,
( aReductOfIn0(sK8(U_43),sK7(U_43),U_43)
| isLocallyConfluent0(U_43)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_14,plain,
( aReductOfIn0(sK9(U_43),sK7(U_43),U_43)
| isLocallyConfluent0(U_43)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_15,plain,
( ~ sdtmndtasgtdt0(sK9(U_43),U_43,U_39)
| ~ sdtmndtasgtdt0(sK8(U_43),U_43,U_39)
| ~ aElement0(U_39)
| isLocallyConfluent0(U_43)
| ~ aRewritingSystem0(U_43) ),
inference(clausify,[status(thm)],[f_11_6]) ).
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]) ).
cnf(f_12_5,plain,
( 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(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( aElement0(sK10(U_48))
| isTerminating0(U_48)
| ~ aRewritingSystem0(U_48) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
( aElement0(sK11(U_48))
| isTerminating0(U_48)
| ~ aRewritingSystem0(U_48) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_8,plain,
( sdtmndtplgtdt0(sK10(U_48),U_48,sK11(U_48))
| isTerminating0(U_48)
| ~ aRewritingSystem0(U_48) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_9,plain,
( ~ iLess0(sK11(U_48),sK10(U_48))
| isTerminating0(U_48)
| ~ aRewritingSystem0(U_48) ),
inference(clausify,[status(thm)],[f_12_4]) ).
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]) ).
cnf(f_13_5,plain,
( aElement0(U_54)
| ~ aNormalFormOfIn0(U_54,U_53,U_52)
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( sdtmndtasgtdt0(U_53,U_52,U_54)
| ~ aNormalFormOfIn0(U_54,U_53,U_52)
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_7,plain,
( ~ aReductOfIn0(U_49,U_54,U_52)
| ~ aNormalFormOfIn0(U_54,U_53,U_52)
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(clausify,[status(thm)],[f_13_4]) ).
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)
| ~ aRewritingSystem0(U_52)
| ~ aElement0(U_53) ),
inference(clausify,[status(thm)],[f_13_4]) ).
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]) ).
cnf(f_14_4,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_3]) ).
fof(f_15_1,plain,
aRewritingSystem0(xR),
inference(fof_nnf,[status(thm)],[m__656]) ).
cnf(f_15_2,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
inference(fof_nnf,[status(thm)],[m__656_01]) ).
cnf(f_16_2,plain,
isLocallyConfluent0(xR),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
isTerminating0(xR),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(fof_nnf,[status(thm)],[m__731]) ).
cnf(f_17_2,plain,
aElement0(xa),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
aElement0(xb),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_4,plain,
aElement0(xc),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& sdtmndtasgtdt0(W1,xR,W3)
& aElement0(W3) )
| ~ iLess0(W0,xa)
| ~ sdtmndtasgtdt0(W0,xR,W2)
| ~ sdtmndtasgtdt0(W0,xR,W1)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[m__715]) ).
fof(f_18_2,plain,
! [U_62,U_61,U_60] :
( ? [U_59] :
( sdtmndtasgtdt0(U_60,xR,U_59)
& sdtmndtasgtdt0(U_61,xR,U_59)
& aElement0(U_59) )
| ~ iLess0(U_62,xa)
| ~ sdtmndtasgtdt0(U_62,xR,U_60)
| ~ sdtmndtasgtdt0(U_62,xR,U_61)
| ~ aElement0(U_60)
| ~ aElement0(U_61)
| ~ aElement0(U_62) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_62,U_61,U_60] :
( ( sdtmndtasgtdt0(U_60,xR,sK14(U_62,U_61,U_60))
& sdtmndtasgtdt0(U_61,xR,sK14(U_62,U_61,U_60))
& aElement0(sK14(U_62,U_61,U_60)) )
| ~ iLess0(U_62,xa)
| ~ sdtmndtasgtdt0(U_62,xR,U_60)
| ~ sdtmndtasgtdt0(U_62,xR,U_61)
| ~ aElement0(U_60)
| ~ aElement0(U_61)
| ~ aElement0(U_62) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_59,sK14(U_62,U_61,U_60))],[f_18_2]) ).
cnf(f_18_4,plain,
( aElement0(sK14(U_62,U_61,U_60))
| ~ iLess0(U_62,xa)
| ~ sdtmndtasgtdt0(U_62,xR,U_60)
| ~ sdtmndtasgtdt0(U_62,xR,U_61)
| ~ aElement0(U_60)
| ~ aElement0(U_61)
| ~ aElement0(U_62) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( sdtmndtasgtdt0(U_61,xR,sK14(U_62,U_61,U_60))
| ~ iLess0(U_62,xa)
| ~ sdtmndtasgtdt0(U_62,xR,U_60)
| ~ sdtmndtasgtdt0(U_62,xR,U_61)
| ~ aElement0(U_60)
| ~ aElement0(U_61)
| ~ aElement0(U_62) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( sdtmndtasgtdt0(U_60,xR,sK14(U_62,U_61,U_60))
| ~ iLess0(U_62,xa)
| ~ sdtmndtasgtdt0(U_62,xR,U_60)
| ~ sdtmndtasgtdt0(U_62,xR,U_61)
| ~ aElement0(U_60)
| ~ aElement0(U_61)
| ~ aElement0(U_62) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
inference(fof_nnf,[status(thm)],[m__731_02]) ).
cnf(f_19_2,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(clausify,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
sdtmndtplgtdt0(xa,xR,xc),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(fof_nnf,[status(thm)],[m__755]) ).
cnf(f_20_2,plain,
aElement0(xu),
inference(clausify,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
aReductOfIn0(xu,xa,xR),
inference(clausify,[status(thm)],[f_20_1]) ).
cnf(f_20_4,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
inference(fof_nnf,[status(thm)],[m__779]) ).
cnf(f_21_2,plain,
aElement0(xv),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
aReductOfIn0(xv,xa,xR),
inference(clausify,[status(thm)],[f_21_1]) ).
cnf(f_21_4,plain,
sdtmndtasgtdt0(xv,xR,xc),
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_22_2,negated_conjecture,
! [W0] :
( ~ sdtmndtasgtdt0(xv,xR,W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[f_22_1]) ).
fof(f_22_3,negated_conjecture,
! [U_63] :
( ~ sdtmndtasgtdt0(xv,xR,U_63)
| ~ sdtmndtasgtdt0(xu,xR,U_63)
| ~ aElement0(U_63) ),
inference(variable_rename,[status(thm)],[f_22_2]) ).
cnf(f_22_4,negated_conjecture,
( ~ sdtmndtasgtdt0(xv,xR,U_63)
| ~ sdtmndtasgtdt0(xu,xR,U_63)
| ~ aElement0(U_63) ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_2_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_4]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
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,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( aRewritingSystem0(Eq_y_0)
| ~ aRewritingSystem0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,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_21,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_22,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_23,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_24,axiom,
( isConfluent0(Eq_y_0)
| ~ isConfluent0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( isLocallyConfluent0(Eq_y_0)
| ~ isLocallyConfluent0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( isTerminating0(Eq_y_0)
| ~ isTerminating0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 15:18:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 102.12/102.49 % SZS status Theorem for theBenchmark
% 102.12/102.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------