%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG101+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 : n009.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 08:55:10 AM UTC 2026
% Result : Theorem 120.45s 120.89s
% Output : Proof 120.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 19 unt; 1 def)
% Number of atoms : 180 ( 60 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 226 ( 86 ~; 80 |; 57 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 0 sgn 51 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefPrIdeal,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('theBenchmark.p',mDefPrIdeal) ).
fof(m__1905,hypothesis,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
fof(m__1933,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
file('theBenchmark.p',m__1933) ).
fof(m__,conjecture,
? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ),
file('theBenchmark.p',m__) ).
fof(f_37_1,plain,
! [W0] :
( ! [W1] :
( ( W1 = slsdtgt0(W0)
| ? [W2] :
( ( ~ aElementOf0(W2,W1)
& ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
| ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
& aElementOf0(W2,W1) ) )
| ~ aSet0(W1) )
& ( ( ! [W2] :
( ( aElementOf0(W2,W1)
| ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) ) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mDefPrIdeal]) ).
fof(f_37_2,plain,
! [U_117] :
( ! [U_116] :
( ( U_116 = slsdtgt0(U_117)
| ? [U_115] :
( ( ~ aElementOf0(U_115,U_116)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_115
& aElement0(U_114) ) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != U_115
| ~ aElement0(U_113) )
& aElementOf0(U_115,U_116) ) )
| ~ aSet0(U_116) )
& ( ( ! [U_112] :
( ( aElementOf0(U_112,U_116)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_112
| ~ aElement0(U_111) ) )
& ( ? [U_110] :
( sdtasdt0(U_117,U_110) = U_112
& aElement0(U_110) )
| ~ aElementOf0(U_112,U_116) ) )
& aSet0(U_116) )
| U_116 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ? [U_121] :
( ~ aElementOf0(U_121,U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_121
& aElement0(U_114) ) )
| ? [U_120] :
( ! [U_113] :
( sdtasdt0(U_117,U_113) != U_120
| ~ aElement0(U_113) )
& aElementOf0(U_120,U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ? [U_110] :
( sdtasdt0(U_117,U_110) = U_118
& aElement0(U_110) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ? [U_121] :
( ~ aElementOf0(U_121,U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_121
& aElement0(U_114) ) )
| ? [U_120] :
( ! [U_113] :
( sdtasdt0(U_117,U_113) != U_120
| ~ aElement0(U_113) )
& aElementOf0(U_120,U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_110,sK20(U_117,U_122,U_118))],[f_37_3]) ).
fof(f_37_5,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ? [U_121] :
( ~ aElementOf0(U_121,U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = U_121
& aElement0(U_114) ) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113) )
& aElementOf0(sK21(U_117,U_123),U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_120,sK21(U_117,U_123))],[f_37_4]) ).
fof(f_37_6,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ( ~ aElementOf0(sK22(U_117,U_123),U_123)
& ? [U_114] :
( sdtasdt0(U_117,U_114) = sK22(U_117,U_123)
& aElement0(U_114) ) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113) )
& aElementOf0(sK21(U_117,U_123),U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_121,sK22(U_117,U_123))],[f_37_5]) ).
fof(f_37_7,plain,
! [U_117] :
( ( ! [U_123] :
( U_123 = slsdtgt0(U_117)
| ( ~ aElementOf0(sK22(U_117,U_123),U_123)
& sdtasdt0(U_117,sK23(U_117,U_123)) = sK22(U_117,U_123)
& aElement0(sK23(U_117,U_123)) )
| ( ! [U_113] :
( sdtasdt0(U_117,U_113) != sK21(U_117,U_123)
| ~ aElement0(U_113) )
& aElementOf0(sK21(U_117,U_123),U_123) )
| ~ aSet0(U_123) )
& ! [U_122] :
( ( ! [U_119] :
( aElementOf0(U_119,U_122)
| ! [U_111] :
( sdtasdt0(U_117,U_111) != U_119
| ~ aElement0(U_111) ) )
& ! [U_118] :
( ( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
& aElement0(sK20(U_117,U_122,U_118)) )
| ~ aElementOf0(U_118,U_122) )
& aSet0(U_122) )
| U_122 != slsdtgt0(U_117) ) )
| ~ aElement0(U_117) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_114,sK23(U_117,U_123))],[f_37_6]) ).
cnf(f_37_9,plain,
( aElement0(sK20(U_117,U_122,U_118))
| ~ aElementOf0(U_118,U_122)
| U_122 != slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(f_37_10,plain,
( sdtasdt0(U_117,sK20(U_117,U_122,U_118)) = U_118
| ~ aElementOf0(U_118,U_122)
| U_122 != slsdtgt0(U_117)
| ~ aElement0(U_117) ),
inference(clausify,[status(thm)],[f_37_7]) ).
fof(f_38_1,plain,
aElement0(xc),
inference(fof_nnf,[status(thm)],[m__1905]) ).
cnf(f_38_2,plain,
aElement0(xc),
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
inference(fof_nnf,[status(thm)],[m__1933]) ).
cnf(f_39_2,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xc,W0) = xx
& aElement0(W0) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_40_2,negated_conjecture,
! [W0] :
( sdtasdt0(xc,W0) != xx
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[f_40_1]) ).
fof(f_40_3,negated_conjecture,
! [U_124] :
( sdtasdt0(xc,U_124) != xx
| ~ aElement0(U_124) ),
inference(variable_rename,[status(thm)],[f_40_2]) ).
fof(f_40_4,negated_conjecture,
! [U_124] :
( sdtasdt0(xc,U_124) != xx
| ~ aElement0(U_124) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,negated_conjecture,
( sdtasdt0(xc,U_124) != xx
| ~ aElement0(U_124) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( sdtasdt0(xc,sK20(xc,slsdtgt0(xc),xx)) != xx
| ~ aElement0(sK20(xc,slsdtgt0(xc),xx)) ),
inference(start,[status(thm),parent(0:0)],[f_40_5]) ).
cnf(t2,plain,
( slsdtgt0(xc) != slsdtgt0(xc)
| ~ aElementOf0(xx,slsdtgt0(xc))
| ~ aElement0(xc)
| aElement0(sK20(xc,slsdtgt0(xc),xx)) ),
inference(extension,[status(thm),parent(t1:1)],[f_37_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aElement0(xc),
inference(extension,[status(thm),parent(t2:2)],[f_38_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t2:3)],[f_39_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
slsdtgt0(xc) = slsdtgt0(xc),
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
( slsdtgt0(xc) != slsdtgt0(xc)
| ~ aElementOf0(xx,slsdtgt0(xc))
| ~ aElement0(xc)
| sdtasdt0(xc,sK20(xc,slsdtgt0(xc),xx)) = xx ),
inference(extension,[status(thm),parent(t1:2)],[f_37_10]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
aElement0(xc),
inference(extension,[status(thm),parent(t10:2)],[f_38_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
aElementOf0(xx,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t10:3)],[f_39_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
slsdtgt0(xc) = slsdtgt0(xc),
inference(extension,[status(thm),parent(t10:4)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG101+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
% 0.09/0.46 % Computer : n009.cluster.edu
% 0.09/0.46 % Model : x86_64 x86_64
% 0.09/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.46 % Memory : 8046.5625MB
% 0.09/0.46 % OS : Linux 6.8.0-71-generic
% 0.09/0.46 % CPULimit : 300
% 0.09/0.46 % WCLimit : 300
% 0.09/0.46 % DateTime : Sat Sep 19 20:53:42 UTC 2026
% 0.09/0.46 % CPUTime :
% 120.45/120.89 % SZS status Theorem for theBenchmark
% 120.45/120.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------