%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM018+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 : n004.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 13.58s 13.83s
% Output : Proof 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 14 unt; 0 def)
% Number of atoms : 369 ( 29 equ)
% Maximal formula atoms : 30 ( 9 avg)
% Number of connectives : 461 ( 130 ~; 146 |; 180 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 101 ( 1 sgn 66 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
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__799,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xv,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xu,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('theBenchmark.p',m__799) ).
fof(m__,conjecture,
? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
file('theBenchmark.p',m__) ).
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)
& ! [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]) ).
cnf(f_16_21,plain,
isTerminating0(xR),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_22_1,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xv,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xw)
& aReductOfIn0(W0,xu,xR)
& aElement0(W0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(fof_nnf,[status(thm)],[m__799]) ).
fof(f_22_2,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [U_81] :
( sdtmndtplgtdt0(U_81,xR,xw)
& aReductOfIn0(U_81,xv,xR)
& aElement0(U_81) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [U_80] :
( sdtmndtplgtdt0(U_80,xR,xw)
& aReductOfIn0(U_80,xu,xR)
& aElement0(U_80) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [U_81] :
( sdtmndtplgtdt0(U_81,xR,xw)
& aReductOfIn0(U_81,xv,xR)
& aElement0(U_81) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK24,xR,xw)
& aReductOfIn0(sK24,xu,xR)
& aElement0(sK24) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_80,sK24)],[f_22_2]) ).
fof(f_22_4,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK25,xR,xw)
& aReductOfIn0(sK25,xv,xR)
& aElement0(sK25) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK24,xR,xw)
& aReductOfIn0(sK24,xu,xR)
& aElement0(sK24) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_81,sK25)],[f_22_3]) ).
cnf(f_22_5,plain,
aElement0(xw),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,negated_conjecture,
~ ? [W0] :
( aNormalFormOfIn0(W0,xw,xR)
| ( ~ ? [W1] : aReductOfIn0(W1,W0,xR)
& ( sdtmndtasgtdt0(xw,xR,W0)
| sdtmndtplgtdt0(xw,xR,W0)
| ? [W1] :
( sdtmndtplgtdt0(W1,xR,W0)
& aReductOfIn0(W1,xw,xR)
& aElement0(W1) )
| aReductOfIn0(W0,xw,xR)
| xw = W0 )
& aElement0(W0) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_23_2,negated_conjecture,
! [W0] :
( ~ aNormalFormOfIn0(W0,xw,xR)
& ( ? [W1] : aReductOfIn0(W1,W0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ! [W1] :
( ~ sdtmndtplgtdt0(W1,xR,W0)
| ~ aReductOfIn0(W1,xw,xR)
| ~ aElement0(W1) )
& ~ aReductOfIn0(W0,xw,xR)
& xw != W0 )
| ~ aElement0(W0) ) ),
inference(fof_nnf,[status(thm)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
! [U_84] :
( ~ aNormalFormOfIn0(U_84,xw,xR)
& ( ? [U_83] : aReductOfIn0(U_83,U_84,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,U_84)
& ~ sdtmndtplgtdt0(xw,xR,U_84)
& ! [U_82] :
( ~ sdtmndtplgtdt0(U_82,xR,U_84)
| ~ aReductOfIn0(U_82,xw,xR)
| ~ aElement0(U_82) )
& ~ aReductOfIn0(U_84,xw,xR)
& xw != U_84 )
| ~ aElement0(U_84) ) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
( ! [U_86] : ~ aNormalFormOfIn0(U_86,xw,xR)
& ! [U_85] :
( ? [U_83] : aReductOfIn0(U_83,U_85,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,U_85)
& ~ sdtmndtplgtdt0(xw,xR,U_85)
& ! [U_82] :
( ~ sdtmndtplgtdt0(U_82,xR,U_85)
| ~ aReductOfIn0(U_82,xw,xR)
| ~ aElement0(U_82) )
& ~ aReductOfIn0(U_85,xw,xR)
& xw != U_85 )
| ~ aElement0(U_85) ) ),
inference(miniscope,[status(thm)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
( ! [U_86] : ~ aNormalFormOfIn0(U_86,xw,xR)
& ! [U_85] :
( aReductOfIn0(sK26(U_85),U_85,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,U_85)
& ~ sdtmndtplgtdt0(xw,xR,U_85)
& ! [U_82] :
( ~ sdtmndtplgtdt0(U_82,xR,U_85)
| ~ aReductOfIn0(U_82,xw,xR)
| ~ aElement0(U_82) )
& ~ aReductOfIn0(U_85,xw,xR)
& xw != U_85 )
| ~ aElement0(U_85) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_83,sK26(U_85))],[f_23_4]) ).
fof(f_23_6,negated_conjecture,
( ! [U_82,U_85] :
( ~ sdtmndtasgtdt0(xw,xR,U_85)
| ~ sP0(U_82,U_85) )
& ! [U_82,U_85] :
( ~ sdtmndtplgtdt0(xw,xR,U_85)
| ~ sP0(U_82,U_85) )
& ! [U_82,U_85] :
( ~ sdtmndtplgtdt0(U_82,xR,U_85)
| ~ aReductOfIn0(U_82,xw,xR)
| ~ aElement0(U_82)
| ~ sP0(U_82,U_85) )
& ! [U_82,U_85] :
( ~ aReductOfIn0(U_85,xw,xR)
| ~ sP0(U_82,U_85) )
& ! [U_82,U_85] :
( xw != U_85
| ~ sP0(U_82,U_85) )
& ! [U_86] : ~ aNormalFormOfIn0(U_86,xw,xR)
& ! [U_82,U_85] :
( aReductOfIn0(sK26(U_85),U_85,xR)
| sP0(U_82,U_85)
| ~ aElement0(U_85) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_23_5]) ).
cnf(f_23_8,negated_conjecture,
~ aNormalFormOfIn0(U_86,xw,xR),
inference(clausify,[status(thm)],[f_23_6]) ).
cnf(t1,plain,
~ aNormalFormOfIn0(sK13(xR,xw),xw,xR),
inference(start,[status(thm),parent(0:0)],[f_23_8]) ).
cnf(t2,plain,
( ~ isTerminating0(xR)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(sK13(xR,xw),xw,xR) ),
inference(extension,[status(thm),parent(t1:1)],[f_14_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aRewritingSystem0(xR),
inference(extension,[status(thm),parent(t2:2)],[f_15_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aElement0(xw),
inference(extension,[status(thm),parent(t2:3)],[f_22_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
isTerminating0(xR),
inference(extension,[status(thm),parent(t2:4)],[f_16_21]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n004.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sun Sep 20 15:07:52 UTC 2026
% 0.20/0.44 % CPUTime :
% 13.58/13.83 % SZS status Theorem for theBenchmark
% 13.58/13.83 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------