%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG088+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 : n020.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 0.14s 5.50s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 92 ( 4 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 90 ( 29 ~; 24 |; 31 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 18 !; 0 ?)
% 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__934,hypothesis,
( xx = sdtpldt0(xk,xl)
& aElementOf0(xl,xJ)
& aElementOf0(xk,xI) ),
file('theBenchmark.p',m__934) ).
fof(m__967,hypothesis,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
file('theBenchmark.p',m__967) ).
fof(m__,conjecture,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),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_4,plain,
( aElementOf0(sdtpldt0(U_74,U_72),xI)
| ~ aElementOf0(U_72,xI)
| ~ aElementOf0(U_74,xI) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_8,plain,
( aElementOf0(sdtpldt0(U_77,U_75),xJ)
| ~ aElementOf0(U_75,xJ)
| ~ aElementOf0(U_77,xJ) ),
inference(clausify,[status(thm)],[f_25_2]) ).
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_28_1,plain,
( xy = sdtpldt0(xm,xn)
& aElementOf0(xn,xJ)
& aElementOf0(xm,xI) ),
inference(fof_nnf,[status(thm)],[m__967]) ).
cnf(f_28_2,plain,
aElementOf0(xm,xI),
inference(clausify,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
aElementOf0(xn,xJ),
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_29_2,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(fof_nnf,[status(thm)],[f_29_1]) ).
fof(f_29_3,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(t1,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(start,[status(thm),parent(0:0)],[f_29_4]) ).
cnf(t2,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(extension,[status(thm),parent(t1:1)],[f_25_4]) ).
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,
aElementOf0(xm,xI),
inference(extension,[status(thm),parent(t2:3)],[f_28_2]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ)
| aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(extension,[status(thm),parent(t1:2)],[f_25_8]) ).
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,
aElementOf0(xn,xJ),
inference(extension,[status(thm),parent(t8:3)],[f_28_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG088+2 : 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
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 19 20:51:37 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.14/5.50 % SZS status Theorem for theBenchmark
% 0.14/5.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------