%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG089+2 : 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 : n015.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 08:55:08 AM UTC 2026
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 157 ( 18 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 150 ( 29 ~; 24 |; 91 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 18 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__870,hypothesis,
( aIdeal0(xJ)
& ! [W0] :
( aElementOf0(W0,xJ)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) )
& ! [W1] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) ) ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( aElementOf0(W0,xI)
=> ( ! [W1] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) )
& ! [W1] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) ) ) )
& aSet0(xI) ),
file('theBenchmark.p',m__870) ).
fof(m__901,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
file('theBenchmark.p',m__901) ).
fof(m__934,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('theBenchmark.p',m__934) ).
fof(m__,conjecture,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('theBenchmark.p',m__) ).
fof(f_25_1,plain,
( aIdeal0(xJ)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xJ)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xJ)
| ~ aElementOf0(W1,xJ) ) )
| ~ aElementOf0(W0,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [W0] :
( ( ! [W1] :
( aElementOf0(sdtasdt0(W1,W0),xI)
| ~ aElement0(W1) )
& ! [W1] :
( aElementOf0(sdtpldt0(W0,W1),xI)
| ~ aElementOf0(W1,xI) ) )
| ~ aElementOf0(W0,xI) )
& aSet0(xI) ),
inference(fof_nnf,[status(thm)],[m__870]) ).
fof(f_25_2,plain,
( aIdeal0(xJ)
& ! [U_77] :
( ( ! [U_76] :
( aElementOf0(sdtasdt0(U_76,U_77),xJ)
| ~ aElement0(U_76) )
& ! [U_75] :
( aElementOf0(sdtpldt0(U_77,U_75),xJ)
| ~ aElementOf0(U_75,xJ) ) )
| ~ aElementOf0(U_77,xJ) )
& aSet0(xJ)
& aIdeal0(xI)
& ! [U_74] :
( ( ! [U_73] :
( aElementOf0(sdtasdt0(U_73,U_74),xI)
| ~ aElement0(U_73) )
& ! [U_72] :
( aElementOf0(sdtpldt0(U_74,U_72),xI)
| ~ aElementOf0(U_72,xI) ) )
| ~ aElementOf0(U_74,xI) )
& aSet0(xI) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_5,plain,
( aElementOf0(sdtasdt0(U_73,U_74),xI)
| ~ aElement0(U_73)
| ~ aElementOf0(U_74,xI) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_9,plain,
( aElementOf0(sdtasdt0(U_76,U_77),xJ)
| ~ aElement0(U_76)
| ~ aElementOf0(U_77,xJ) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xy
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [W0,W1] :
( sdtpldt0(W0,W1) = xx
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ),
inference(fof_nnf,[status(thm)],[m__901]) ).
fof(f_26_2,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [U_81,U_80] :
( sdtpldt0(U_81,U_80) = xy
& aElementOf0(U_80,xJ)
& aElementOf0(U_81,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [U_79,U_78] :
( sdtpldt0(U_79,U_78) = xx
& aElementOf0(U_78,xJ)
& aElementOf0(U_79,xI) ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [U_81] :
( ? [U_80] :
( sdtpldt0(U_81,U_80) = xy
& aElementOf0(U_80,xJ) )
& aElementOf0(U_81,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [U_79] :
( ? [U_78] :
( sdtpldt0(U_79,U_78) = xx
& aElementOf0(U_78,xJ) )
& aElementOf0(U_79,xI) ) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [U_81] :
( ? [U_80] :
( sdtpldt0(U_81,U_80) = xy
& aElementOf0(U_80,xJ) )
& aElementOf0(U_81,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [U_78] :
( sdtpldt0(sK14,U_78) = xx
& aElementOf0(U_78,xJ) )
& aElementOf0(sK14,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_79,sK14)],[f_26_3]) ).
fof(f_26_5,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [U_81] :
( ? [U_80] :
( sdtpldt0(U_81,U_80) = xy
& aElementOf0(U_80,xJ) )
& aElementOf0(U_81,xI) )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& sdtpldt0(sK14,sK15) = xx
& aElementOf0(sK15,xJ)
& aElementOf0(sK14,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_78,sK15)],[f_26_4]) ).
fof(f_26_6,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& ? [U_80] :
( sdtpldt0(sK16,U_80) = xy
& aElementOf0(U_80,xJ) )
& aElementOf0(sK16,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& sdtpldt0(sK14,sK15) = xx
& aElementOf0(sK15,xJ)
& aElementOf0(sK14,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_81,sK16)],[f_26_5]) ).
fof(f_26_7,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& sdtpldt0(sK16,sK17) = xy
& aElementOf0(sK17,xJ)
& aElementOf0(sK16,xI)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& sdtpldt0(sK14,sK15) = xx
& aElementOf0(sK15,xJ)
& aElementOf0(sK14,xI) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_80,sK17)],[f_26_6]) ).
cnf(f_26_16,plain,
aElement0(xz),
inference(clausify,[status(thm)],[f_26_7]) ).
fof(f_27_1,plain,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
inference(fof_nnf,[status(thm)],[m__934]) ).
cnf(f_27_2,plain,
aElementOf0(xk,xI),
inference(clausify,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
aElementOf0(xl,xJ),
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_30_1,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_30_2,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(fof_nnf,[status(thm)],[f_30_1]) ).
fof(f_30_3,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,negated_conjecture,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(t1,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(start,[status(thm),parent(0:0)],[f_30_4]) ).
cnf(t2,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(extension,[status(thm),parent(t1:1)],[f_25_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aElementOf0(xk,xI),
inference(extension,[status(thm),parent(t2:2)],[f_27_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
aElement0(xz),
inference(extension,[status(thm),parent(t2:3)],[f_26_16]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(extension,[status(thm),parent(t1:2)],[f_25_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:2]) ).
cnf(t10,plain,
aElementOf0(xl,xJ),
inference(extension,[status(thm),parent(t8:2)],[f_27_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
aElement0(xz),
inference(extension,[status(thm),parent(t8:3)],[f_26_16]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 20:54:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------