%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM018+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 0.22s 0.58s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 19 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 21 ~; 15 |; 7 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 1 sgn 11 !; 5 ?)
% 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)
& isLocallyConfluent0(xR) ),
file('theBenchmark.p',m__656_01) ).
fof(m__799,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
file('theBenchmark.p',m__799) ).
fof(m__,conjecture,
? [W0] : aNormalFormOfIn0(W0,xw,xR),
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)
& isLocallyConfluent0(xR) ),
inference(fof_nnf,[status(thm)],[m__656_01]) ).
cnf(f_16_3,plain,
isTerminating0(xR),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_22_1,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
inference(fof_nnf,[status(thm)],[m__799]) ).
cnf(f_22_2,plain,
aElement0(xw),
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,negated_conjecture,
~ ? [W0] : aNormalFormOfIn0(W0,xw,xR),
inference(negate,[status(cth)],[m__]) ).
fof(f_23_2,negated_conjecture,
! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(fof_nnf,[status(thm)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
! [U_63] : ~ aNormalFormOfIn0(U_63,xw,xR),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
! [U_63] : ~ aNormalFormOfIn0(U_63,xw,xR),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,negated_conjecture,
~ aNormalFormOfIn0(U_63,xw,xR),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(t1,plain,
~ aNormalFormOfIn0(sK13(xR,xw),xw,xR),
inference(start,[status(thm),parent(0:0)],[f_23_5]) ).
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_2]) ).
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_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n016.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 15:12:37 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.22/0.58 % SZS status Theorem for theBenchmark
% 0.22/0.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------