%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG089+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 : n001.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 0.10s 0.42s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 19 unt; 1 def)
% Number of atoms : 150 ( 2 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 169 ( 60 ~; 55 |; 50 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 32 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefIdeal,definition,
! [W0] :
( aIdeal0(W0)
<=> ( ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) )
& ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) ) ) )
& aSet0(W0) ) ),
file('theBenchmark.p',mDefIdeal) ).
fof(m__870,hypothesis,
( aIdeal0(xJ)
& aIdeal0(xI) ),
file('theBenchmark.p',m__870) ).
fof(m__901,hypothesis,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
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_24_1,plain,
! [W0] :
( ( aIdeal0(W0)
| ? [W1] :
( ( ? [W2] :
( ~ aElementOf0(sdtasdt0(W2,W1),W0)
& aElement0(W2) )
| ? [W2] :
( ~ aElementOf0(sdtpldt0(W1,W2),W0)
& aElementOf0(W2,W0) ) )
& aElementOf0(W1,W0) )
| ~ aSet0(W0) )
& ( ( ! [W1] :
( ( ! [W2] :
( aElementOf0(sdtasdt0(W2,W1),W0)
| ~ aElement0(W2) )
& ! [W2] :
( aElementOf0(sdtpldt0(W1,W2),W0)
| ~ aElementOf0(W2,W0) ) )
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aIdeal0(W0) ) ),
inference(fof_nnf,[status(thm)],[mDefIdeal]) ).
fof(f_24_2,plain,
! [U_69] :
( ( aIdeal0(U_69)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_69)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_69)
& aElementOf0(U_66,U_69) ) )
& aElementOf0(U_68,U_69) )
| ~ aSet0(U_69) )
& ( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_69)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_69)
| ~ aElementOf0(U_63,U_69) ) )
| ~ aElementOf0(U_65,U_69) )
& aSet0(U_69) )
| ~ aIdeal0(U_69) ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ? [U_68] :
( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,U_68),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(U_68,U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(U_68,U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ? [U_66] :
( ~ aElementOf0(sdtpldt0(sK11(U_71),U_66),U_71)
& aElementOf0(U_66,U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_68,sK11(U_71))],[f_24_3]) ).
fof(f_24_5,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ? [U_67] :
( ~ aElementOf0(sdtasdt0(U_67,sK11(U_71)),U_71)
& aElement0(U_67) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_66,sK12(U_71))],[f_24_4]) ).
fof(f_24_6,plain,
( ! [U_71] :
( aIdeal0(U_71)
| ( ( ( ~ aElementOf0(sdtasdt0(sK13(U_71),sK11(U_71)),U_71)
& aElement0(sK13(U_71)) )
| ( ~ aElementOf0(sdtpldt0(sK11(U_71),sK12(U_71)),U_71)
& aElementOf0(sK12(U_71),U_71) ) )
& aElementOf0(sK11(U_71),U_71) )
| ~ aSet0(U_71) )
& ! [U_70] :
( ( ! [U_65] :
( ( ! [U_64] :
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64) )
& ! [U_63] :
( aElementOf0(sdtpldt0(U_65,U_63),U_70)
| ~ aElementOf0(U_63,U_70) ) )
| ~ aElementOf0(U_65,U_70) )
& aSet0(U_70) )
| ~ aIdeal0(U_70) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_67,sK13(U_71))],[f_24_5]) ).
cnf(f_24_9,plain,
( aElementOf0(sdtasdt0(U_64,U_65),U_70)
| ~ aElement0(U_64)
| ~ aElementOf0(U_65,U_70)
| ~ aIdeal0(U_70) ),
inference(clausify,[status(thm)],[f_24_6]) ).
fof(f_25_1,plain,
( aIdeal0(xJ)
& aIdeal0(xI) ),
inference(fof_nnf,[status(thm)],[m__870]) ).
cnf(f_25_2,plain,
aIdeal0(xI),
inference(clausify,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
aIdeal0(xJ),
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
( aElement0(xz)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElementOf0(xx,sdtpldt1(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[m__901]) ).
cnf(f_26_4,plain,
aElement0(xz),
inference(clausify,[status(thm)],[f_26_1]) ).
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,
( ~ aElementOf0(xk,xI)
| ~ aElement0(xz)
| ~ aIdeal0(xI)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(extension,[status(thm),parent(t1:1)],[f_24_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
aIdeal0(xI),
inference(extension,[status(thm),parent(t2:2)],[f_25_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_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
aElementOf0(xk,xI),
inference(extension,[status(thm),parent(t2:4)],[f_27_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
( ~ aElementOf0(xl,xJ)
| ~ aElement0(xz)
| ~ aIdeal0(xJ)
| aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(extension,[status(thm),parent(t1:2)],[f_24_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
aIdeal0(xJ),
inference(extension,[status(thm),parent(t10:2)],[f_25_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
aElement0(xz),
inference(extension,[status(thm),parent(t10:3)],[f_26_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
aElementOf0(xl,xJ),
inference(extension,[status(thm),parent(t10:4)],[f_27_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG089+1 : 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
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 20:56:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------