%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG087+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 : n006.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 120.63s 130.99s
% Output : Proof 120.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 110 ( 30 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 103 ( 21 ~; 14 |; 68 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 8 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
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__,conjecture,
? [W0,W1] :
( xy = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
file('theBenchmark.p',m__) ).
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_12,plain,
aElementOf0(sK16,xI),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_13,plain,
aElementOf0(sK17,xJ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(f_26_14,plain,
sdtpldt0(sK16,sK17) = xy,
inference(clausify,[status(thm)],[f_26_7]) ).
fof(f_28_1,negated_conjecture,
~ ? [W0,W1] :
( xy = sdtpldt0(W0,W1)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_28_2,negated_conjecture,
! [W0,W1] :
( xy != sdtpldt0(W0,W1)
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ),
inference(fof_nnf,[status(thm)],[f_28_1]) ).
fof(f_28_3,negated_conjecture,
! [U_83,U_82] :
( xy != sdtpldt0(U_83,U_82)
| ~ aElementOf0(U_82,xJ)
| ~ aElementOf0(U_83,xI) ),
inference(variable_rename,[status(thm)],[f_28_2]) ).
fof(f_28_4,negated_conjecture,
! [U_83] :
( ! [U_82] :
( xy != sdtpldt0(U_83,U_82)
| ~ aElementOf0(U_82,xJ) )
| ~ aElementOf0(U_83,xI) ),
inference(miniscope,[status(thm)],[f_28_3]) ).
fof(f_28_5,negated_conjecture,
! [U_83,U_82] :
( xy != sdtpldt0(U_83,U_82)
| ~ aElementOf0(U_82,xJ)
| ~ aElementOf0(U_83,xI) ),
inference(definitional_conversion,[status(esa)],[f_28_4]) ).
cnf(f_28_6,negated_conjecture,
( xy != sdtpldt0(U_83,U_82)
| ~ aElementOf0(U_82,xJ)
| ~ aElementOf0(U_83,xI) ),
inference(clausify,[status(thm)],[f_28_5]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( ~ aElementOf0(sK17,xJ)
| xy != sdtpldt0(sK16,sK17)
| ~ aElementOf0(sK16,xI) ),
inference(start,[status(thm),parent(0:0)],[f_28_6]) ).
cnf(t2,plain,
aElementOf0(sK16,xI),
inference(extension,[status(thm),parent(t1:1)],[f_26_12]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sdtpldt0(sK16,sK17) != xy
| xy = sdtpldt0(sK16,sK17) ),
inference(extension,[status(thm),parent(t1:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
sdtpldt0(sK16,sK17) = xy,
inference(extension,[status(thm),parent(t4:2)],[f_26_14]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
aElementOf0(sK17,xJ),
inference(extension,[status(thm),parent(t1:3)],[f_26_13]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t1:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG087+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
% 0.11/10.40 % Computer : n006.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Sat Sep 19 20:50:39 UTC 2026
% 0.11/10.40 % CPUTime :
% 120.63/130.99 % SZS status Theorem for theBenchmark
% 120.63/130.99 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------