%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG106+2 : 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 08:55:12 AM UTC 2026
% Result : Theorem 101.53s 101.89s
% Output : Proof 101.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 68 ( 38 unt; 0 def)
% Number of atoms : 496 ( 128 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 601 ( 173 ~; 136 |; 280 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 172 ( 2 sgn 100 !; 66 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__1905,hypothesis,
aElement0(xc),
file('theBenchmark.p',m__1905) ).
fof(m__,conjecture,
( ! [W0,W1,W2] :
( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W1
& aElement0(W3) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) )
=> ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) ) )
=> ( ( ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
<=> ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) ) )
& aSet0(slsdtgt0(xc)) )
=> ( aIdeal0(slsdtgt0(xc))
| ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc)) ) ) ) ) ) ),
file('theBenchmark.p',m__) ).
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,negated_conjecture,
( ~ ( aIdeal0(slsdtgt0(xc))
| ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc)) )
& ! [W1] :
( aElementOf0(W1,slsdtgt0(xc))
=> aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc)) ) ) ) )
& ! [W0] :
( aElementOf0(W0,slsdtgt0(xc))
<=> ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) ) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ( aElement0(W2)
& ( aElementOf0(W1,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W1
& aElement0(W3) ) )
& ( aElementOf0(W0,slsdtgt0(xc))
| ? [W3] :
( sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) )
=> ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_39_2,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [W0] :
( ( ? [W1] :
( ~ aElementOf0(sdtasdt0(W1,W0),slsdtgt0(xc))
& aElement0(W1) )
| ? [W1] :
( ~ aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& aElementOf0(W1,slsdtgt0(xc)) ) )
& aElementOf0(W0,slsdtgt0(xc)) )
& ! [W0] :
( ( aElementOf0(W0,slsdtgt0(xc))
| ! [W1] :
( sdtasdt0(xc,W1) != W0
| ~ aElement0(W1) ) )
& ( ? [W1] :
( sdtasdt0(xc,W1) = W0
& aElement0(W1) )
| ~ aElementOf0(W0,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ! [W0,W1,W2] :
( ? [W3] :
( ? [W4] :
( aElementOf0(sdtasdt0(W2,W0),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtasdt0(W2,W0)
& aElement0(W5) )
& aElementOf0(sdtpldt0(W0,W1),slsdtgt0(xc))
& ? [W5] :
( sdtasdt0(xc,W5) = sdtpldt0(W0,W1)
& aElement0(W5) )
& sdtasdt0(W2,W0) = sdtasdt0(xc,sdtasdt0(W3,W2))
& sdtpldt0(W0,W1) = sdtasdt0(xc,sdtpldt0(W3,W4))
& sdtasdt0(xc,W4) = W1
& aElement0(W4) )
& sdtasdt0(xc,W3) = W0
& aElement0(W3) )
| ~ aElement0(W2)
| ( ~ aElementOf0(W1,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W1
| ~ aElement0(W3) ) )
| ( ~ aElementOf0(W0,slsdtgt0(xc))
& ! [W3] :
( sdtasdt0(xc,W3) != W0
| ~ aElement0(W3) ) ) ) ),
inference(fof_nnf,[status(thm)],[f_39_1]) ).
fof(f_39_3,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_135] :
( ( aElementOf0(U_135,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_135
| ~ aElement0(U_134) ) )
& ( ? [U_133] :
( sdtasdt0(xc,U_133) = U_135
& aElement0(U_133) )
| ~ aElementOf0(U_135,slsdtgt0(xc)) ) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ? [U_129] :
( ? [U_128] :
( aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& ? [U_127] :
( sdtasdt0(xc,U_127) = sdtasdt0(U_130,U_132)
& aElement0(U_127) )
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& ? [U_126] :
( sdtasdt0(xc,U_126) = sdtpldt0(U_132,U_131)
& aElement0(U_126) )
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(U_129,U_130))
& sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(U_129,U_128))
& sdtasdt0(xc,U_128) = U_131
& aElement0(U_128) )
& sdtasdt0(xc,U_129) = U_132
& aElement0(U_129) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(variable_rename,[status(thm)],[f_39_2]) ).
fof(f_39_4,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ? [U_133] :
( sdtasdt0(xc,U_133) = U_139
& aElement0(U_133) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ? [U_129] :
( ? [U_128] :
( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(U_129,U_128))
& sdtasdt0(xc,U_128) = U_131
& aElement0(U_128) )
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& ? [U_127] :
( sdtasdt0(xc,U_127) = sdtasdt0(U_130,U_132)
& aElement0(U_127) )
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& ? [U_126] :
( sdtasdt0(xc,U_126) = sdtpldt0(U_132,U_131)
& aElement0(U_126) )
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(U_129,U_130))
& sdtasdt0(xc,U_129) = U_132
& aElement0(U_129) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(miniscope,[status(thm)],[f_39_3]) ).
fof(f_39_5,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ? [U_133] :
( sdtasdt0(xc,U_133) = U_139
& aElement0(U_133) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( ? [U_128] :
( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),U_128))
& sdtasdt0(xc,U_128) = U_131
& aElement0(U_128) )
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& ? [U_127] :
( sdtasdt0(xc,U_127) = sdtasdt0(U_130,U_132)
& aElement0(U_127) )
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& ? [U_126] :
( sdtasdt0(xc,U_126) = sdtpldt0(U_132,U_131)
& aElement0(U_126) )
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_129,sK24(U_132,U_131,U_130))],[f_39_4]) ).
fof(f_39_6,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ? [U_133] :
( sdtasdt0(xc,U_133) = U_139
& aElement0(U_133) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( ? [U_128] :
( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),U_128))
& sdtasdt0(xc,U_128) = U_131
& aElement0(U_128) )
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& ? [U_127] :
( sdtasdt0(xc,U_127) = sdtasdt0(U_130,U_132)
& aElement0(U_127) )
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_126,sK25(U_132,U_131,U_130))],[f_39_5]) ).
fof(f_39_7,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ? [U_133] :
( sdtasdt0(xc,U_133) = U_139
& aElement0(U_133) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( ? [U_128] :
( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),U_128))
& sdtasdt0(xc,U_128) = U_131
& aElement0(U_128) )
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& sdtasdt0(xc,sK26(U_132,U_131,U_130)) = sdtasdt0(U_130,U_132)
& aElement0(sK26(U_132,U_131,U_130))
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_127,sK26(U_132,U_131,U_130))],[f_39_6]) ).
fof(f_39_8,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ? [U_133] :
( sdtasdt0(xc,U_133) = U_139
& aElement0(U_133) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),sK27(U_132,U_131,U_130)))
& sdtasdt0(xc,sK27(U_132,U_131,U_130)) = U_131
& aElement0(sK27(U_132,U_131,U_130))
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& sdtasdt0(xc,sK26(U_132,U_131,U_130)) = sdtasdt0(U_130,U_132)
& aElement0(sK26(U_132,U_131,U_130))
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_128,sK27(U_132,U_131,U_130))],[f_39_7]) ).
fof(f_39_9,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ? [U_138] :
( ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,U_138),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(U_138,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(U_138,slsdtgt0(xc)) )
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ( sdtasdt0(xc,sK28(U_139)) = U_139
& aElement0(sK28(U_139)) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),sK27(U_132,U_131,U_130)))
& sdtasdt0(xc,sK27(U_132,U_131,U_130)) = U_131
& aElement0(sK27(U_132,U_131,U_130))
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& sdtasdt0(xc,sK26(U_132,U_131,U_130)) = sdtasdt0(U_130,U_132)
& aElement0(sK26(U_132,U_131,U_130))
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_133,sK28(U_139))],[f_39_8]) ).
fof(f_39_10,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,sK29),slsdtgt0(xc))
& aElement0(U_137) )
| ? [U_136] :
( ~ aElementOf0(sdtpldt0(sK29,U_136),slsdtgt0(xc))
& aElementOf0(U_136,slsdtgt0(xc)) ) )
& aElementOf0(sK29,slsdtgt0(xc))
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ( sdtasdt0(xc,sK28(U_139)) = U_139
& aElement0(sK28(U_139)) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),sK27(U_132,U_131,U_130)))
& sdtasdt0(xc,sK27(U_132,U_131,U_130)) = U_131
& aElement0(sK27(U_132,U_131,U_130))
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& sdtasdt0(xc,sK26(U_132,U_131,U_130)) = sdtasdt0(U_130,U_132)
& aElement0(sK26(U_132,U_131,U_130))
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_138,sK29)],[f_39_9]) ).
fof(f_39_11,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ( ? [U_137] :
( ~ aElementOf0(sdtasdt0(U_137,sK29),slsdtgt0(xc))
& aElement0(U_137) )
| ( ~ aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc))
& aElementOf0(sK30,slsdtgt0(xc)) ) )
& aElementOf0(sK29,slsdtgt0(xc))
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ( sdtasdt0(xc,sK28(U_139)) = U_139
& aElement0(sK28(U_139)) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),sK27(U_132,U_131,U_130)))
& sdtasdt0(xc,sK27(U_132,U_131,U_130)) = U_131
& aElement0(sK27(U_132,U_131,U_130))
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& sdtasdt0(xc,sK26(U_132,U_131,U_130)) = sdtasdt0(U_130,U_132)
& aElement0(sK26(U_132,U_131,U_130))
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_136,sK30)],[f_39_10]) ).
fof(f_39_12,negated_conjecture,
( ~ aIdeal0(slsdtgt0(xc))
& ( ( ~ aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc))
& aElement0(sK31) )
| ( ~ aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc))
& aElementOf0(sK30,slsdtgt0(xc)) ) )
& aElementOf0(sK29,slsdtgt0(xc))
& ! [U_140] :
( aElementOf0(U_140,slsdtgt0(xc))
| ! [U_134] :
( sdtasdt0(xc,U_134) != U_140
| ~ aElement0(U_134) ) )
& ! [U_139] :
( ( sdtasdt0(xc,sK28(U_139)) = U_139
& aElement0(sK28(U_139)) )
| ~ aElementOf0(U_139,slsdtgt0(xc)) )
& aSet0(slsdtgt0(xc))
& ! [U_132,U_131,U_130] :
( ( sdtpldt0(U_132,U_131) = sdtasdt0(xc,sdtpldt0(sK24(U_132,U_131,U_130),sK27(U_132,U_131,U_130)))
& sdtasdt0(xc,sK27(U_132,U_131,U_130)) = U_131
& aElement0(sK27(U_132,U_131,U_130))
& aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc))
& sdtasdt0(xc,sK26(U_132,U_131,U_130)) = sdtasdt0(U_130,U_132)
& aElement0(sK26(U_132,U_131,U_130))
& aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc))
& sdtasdt0(xc,sK25(U_132,U_131,U_130)) = sdtpldt0(U_132,U_131)
& aElement0(sK25(U_132,U_131,U_130))
& sdtasdt0(U_130,U_132) = sdtasdt0(xc,sdtasdt0(sK24(U_132,U_131,U_130),U_130))
& sdtasdt0(xc,sK24(U_132,U_131,U_130)) = U_132
& aElement0(sK24(U_132,U_131,U_130)) )
| ~ aElement0(U_130)
| ( ~ aElementOf0(U_131,slsdtgt0(xc))
& ! [U_125] :
( sdtasdt0(xc,U_125) != U_131
| ~ aElement0(U_125) ) )
| ( ~ aElementOf0(U_132,slsdtgt0(xc))
& ! [U_124] :
( sdtasdt0(xc,U_124) != U_132
| ~ aElement0(U_124) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_137,sK31)],[f_39_11]) ).
cnf(f_39_36,negated_conjecture,
( ~ aElementOf0(U_131,slsdtgt0(xc))
| ~ aElementOf0(U_132,slsdtgt0(xc))
| ~ aElement0(U_130)
| aElementOf0(sdtpldt0(U_132,U_131),slsdtgt0(xc)) ),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(f_39_48,negated_conjecture,
( ~ aElementOf0(U_131,slsdtgt0(xc))
| ~ aElementOf0(U_132,slsdtgt0(xc))
| ~ aElement0(U_130)
| aElementOf0(sdtasdt0(U_130,U_132),slsdtgt0(xc)) ),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(f_39_65,negated_conjecture,
aElementOf0(sK29,slsdtgt0(xc)),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(f_39_66,negated_conjecture,
( aElement0(sK31)
| aElementOf0(sK30,slsdtgt0(xc)) ),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(f_39_67,negated_conjecture,
( ~ aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc))
| aElementOf0(sK30,slsdtgt0(xc)) ),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(f_39_68,negated_conjecture,
( aElement0(sK31)
| ~ aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc)) ),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(f_39_69,negated_conjecture,
( ~ aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc)) ),
inference(clausify,[status(thm)],[f_39_12]) ).
cnf(t1,plain,
( ~ aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc)) ),
inference(start,[status(thm),parent(0:0)],[f_39_69]) ).
cnf(t2,plain,
( ~ aElement0(sK31)
| ~ aElementOf0(sK29,slsdtgt0(xc))
| ~ aElementOf0(sK30,slsdtgt0(xc))
| aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc)) ),
inference(extension,[status(thm),parent(t1:1)],[f_39_36]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc))
| aElementOf0(sK30,slsdtgt0(xc)) ),
inference(extension,[status(thm),parent(t2:2)],[f_39_67]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ aElement0(sK31)
| ~ aElementOf0(sK29,slsdtgt0(xc))
| ~ aElementOf0(sK29,slsdtgt0(xc))
| aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc)) ),
inference(extension,[status(thm),parent(t4:2)],[f_39_48]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t6:2)],[f_39_65]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(l4,lemma,
aElementOf0(sK29,slsdtgt0(xc)),
inference(lemma,[status(cth),parent(t6:2),below(t4:2)],[t6:2]) ).
cnf(t10,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(lemma_extension,[status(thm),parent(t6:3)],[l4:1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
( aElementOf0(sK30,slsdtgt0(xc))
| aElement0(sK31) ),
inference(extension,[status(thm),parent(t6:4)],[f_39_66]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:4]) ).
cnf(t14,plain,
$false,
inference(reduction,[status(thm),parent(t12:2)],[t12:2,t2:2]) ).
cnf(t15,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t2:3)],[f_39_65]) ).
cnf(t16,plain,
$false,
inference(connection,[status(thm),parent(t15:1)],[t15:1,t2:3]) ).
cnf(l7,lemma,
aElementOf0(sK29,slsdtgt0(xc)),
inference(lemma,[status(cth),parent(t2:3),below(t1:1)],[t2:3]) ).
cnf(t17,plain,
( aElementOf0(sK30,slsdtgt0(xc))
| aElement0(sK31) ),
inference(extension,[status(thm),parent(t2:4)],[f_39_66]) ).
cnf(t18,plain,
$false,
inference(connection,[status(thm),parent(t17:1)],[t17:1,t2:4]) ).
cnf(t19,plain,
( ~ aElement0(xc)
| ~ aElementOf0(sK29,slsdtgt0(xc))
| aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc))
| ~ aElementOf0(sK30,slsdtgt0(xc)) ),
inference(extension,[status(thm),parent(t17:2)],[f_39_36]) ).
cnf(t20,plain,
$false,
inference(connection,[status(thm),parent(t19:1)],[t19:1,t17:2]) ).
cnf(t21,plain,
$false,
inference(reduction,[status(thm),parent(t19:2)],[t19:2,t1:1]) ).
cnf(t22,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(lemma_extension,[status(thm),parent(t19:3)],[l7:1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t19:3]) ).
cnf(t24,plain,
aElement0(xc),
inference(extension,[status(thm),parent(t19:4)],[f_38_2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t19:4]) ).
cnf(l1,lemma,
aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t26,plain,
( ~ aElement0(sK31)
| ~ aElementOf0(sK29,slsdtgt0(xc))
| ~ aElementOf0(sK30,slsdtgt0(xc))
| aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc)) ),
inference(extension,[status(thm),parent(t1:2)],[f_39_48]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t1:2]) ).
cnf(t28,plain,
( aElement0(sK31)
| aElementOf0(sK30,slsdtgt0(xc)) ),
inference(extension,[status(thm),parent(t26:2)],[f_39_66]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ aElementOf0(sK29,slsdtgt0(xc))
| ~ aElementOf0(sK29,slsdtgt0(xc))
| aElementOf0(sdtasdt0(sK31,sK29),slsdtgt0(xc))
| ~ aElement0(sK31) ),
inference(extension,[status(thm),parent(t28:2)],[f_39_48]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
$false,
inference(reduction,[status(thm),parent(t30:2)],[t30:2,t1:2]) ).
cnf(t33,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t30:3)],[f_39_65]) ).
cnf(t34,plain,
$false,
inference(connection,[status(thm),parent(t33:1)],[t33:1,t30:3]) ).
cnf(t35,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t30:4)],[f_39_65]) ).
cnf(t36,plain,
$false,
inference(connection,[status(thm),parent(t35:1)],[t35:1,t30:4]) ).
cnf(t37,plain,
aElementOf0(sK29,slsdtgt0(xc)),
inference(extension,[status(thm),parent(t26:3)],[f_39_65]) ).
cnf(t38,plain,
$false,
inference(connection,[status(thm),parent(t37:1)],[t37:1,t26:3]) ).
cnf(t39,plain,
( ~ aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc))
| aElement0(sK31) ),
inference(extension,[status(thm),parent(t26:4)],[f_39_68]) ).
cnf(t40,plain,
$false,
inference(connection,[status(thm),parent(t39:1)],[t39:1,t26:4]) ).
cnf(t41,plain,
aElementOf0(sdtpldt0(sK29,sK30),slsdtgt0(xc)),
inference(lemma_extension,[status(thm),parent(t39:2)],[l1:1]) ).
cnf(t42,plain,
$false,
inference(connection,[status(thm),parent(t41:1)],[t41:1,t39:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG106+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 20:58:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 101.53/101.89 % SZS status Theorem for theBenchmark
% 101.53/101.89 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------