%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG091+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 : n008.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 08:55:09 AM UTC 2026
% Result : Theorem 190.13s 200.49s
% Output : Proof 190.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 28 unt; 0 def)
% Number of atoms : 120 ( 32 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 127 ( 56 ~; 45 |; 26 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 42 ( 4 sgn 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
file('theBenchmark.p',m__994) ).
fof(m__1021,hypothesis,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
file('theBenchmark.p',m__1021) ).
fof(m__1061,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('theBenchmark.p',m__1061) ).
fof(m__1098,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('theBenchmark.p',m__1098) ).
fof(m__,conjecture,
( ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtasdt0(xz,xx)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) )
& ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(xx,xy)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ) ),
file('theBenchmark.p',m__) ).
fof(f_29_1,plain,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(fof_nnf,[status(thm)],[m__994]) ).
fof(f_29_2,plain,
( aElementOf0(sdtpldt0(xl,xn),xJ)
& aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(definitional_conversion,[status(esa)],[f_29_1]) ).
cnf(f_29_3,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(fof_nnf,[status(thm)],[m__1021]) ).
fof(f_30_2,plain,
( aElementOf0(sdtasdt0(xz,xl),xJ)
& aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(definitional_conversion,[status(esa)],[f_30_1]) ).
cnf(f_30_3,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(clausify,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(fof_nnf,[status(thm)],[m__1061]) ).
fof(f_31_2,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(definitional_conversion,[status(esa)],[f_31_1]) ).
cnf(f_31_3,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(fof_nnf,[status(thm)],[m__1098]) ).
fof(f_32_2,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(definitional_conversion,[status(esa)],[f_32_1]) ).
cnf(f_32_3,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,negated_conjecture,
~ ( ( aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtasdt0(xz,xx)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) )
& ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ? [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(xx,xy)
& aElementOf0(W1,xJ)
& aElementOf0(W0,xI) ) ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_33_2,negated_conjecture,
( ( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& ! [W0,W1] :
( sdtpldt0(W0,W1) != sdtasdt0(xz,xx)
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& ! [W0,W1] :
( sdtpldt0(W0,W1) != sdtpldt0(xx,xy)
| ~ aElementOf0(W1,xJ)
| ~ aElementOf0(W0,xI) ) ) ),
inference(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
( ( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& ! [U_85,U_84] :
( sdtpldt0(U_85,U_84) != sdtasdt0(xz,xx)
| ~ aElementOf0(U_84,xJ)
| ~ aElementOf0(U_85,xI) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& ! [U_83,U_82] :
( sdtpldt0(U_83,U_82) != sdtpldt0(xx,xy)
| ~ aElementOf0(U_82,xJ)
| ~ aElementOf0(U_83,xI) ) ) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
( ( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
& ! [U_85] :
( ! [U_84] :
( sdtpldt0(U_85,U_84) != sdtasdt0(xz,xx)
| ~ aElementOf0(U_84,xJ) )
| ~ aElementOf0(U_85,xI) ) )
| ( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& ! [U_83] :
( ! [U_82] :
( sdtpldt0(U_83,U_82) != sdtpldt0(xx,xy)
| ~ aElementOf0(U_82,xJ) )
| ~ aElementOf0(U_83,xI) ) ) ),
inference(miniscope,[status(thm)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( ! [U_84,U_85] :
( ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ))
| ~ sP26(U_84,U_85) )
& ! [U_84,U_85] :
( sdtpldt0(U_85,U_84) != sdtasdt0(xz,xx)
| ~ aElementOf0(U_84,xJ)
| ~ aElementOf0(U_85,xI)
| ~ sP26(U_84,U_85) )
& ! [U_83,U_82] :
( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ~ sP25(U_83,U_82) )
& ! [U_83,U_82] :
( sdtpldt0(U_83,U_82) != sdtpldt0(xx,xy)
| ~ aElementOf0(U_82,xJ)
| ~ aElementOf0(U_83,xI)
| ~ sP25(U_83,U_82) )
& ! [U_84,U_85,U_83,U_82] :
( sP26(U_84,U_85)
| sP25(U_83,U_82) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26])],[f_33_4]) ).
cnf(f_33_6,negated_conjecture,
( sP26(U_84,U_85)
| sP25(U_83,U_82) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
( sdtpldt0(U_83,U_82) != sdtpldt0(xx,xy)
| ~ aElementOf0(U_82,xJ)
| ~ aElementOf0(U_83,xI)
| ~ sP25(U_83,U_82) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_9,negated_conjecture,
( sdtpldt0(U_85,U_84) != sdtasdt0(xz,xx)
| ~ aElementOf0(U_84,xJ)
| ~ aElementOf0(U_85,xI)
| ~ sP26(U_84,U_85) ),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
( sP26(sdtasdt0(xz,xl),sdtasdt0(xz,xk))
| sP25(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) ),
inference(start,[status(thm),parent(0:0)],[f_33_6]) ).
cnf(t2,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) != sdtpldt0(xx,xy)
| ~ sP25(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) ),
inference(extension,[status(thm),parent(t1:1)],[f_33_7]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn))
| sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xx,xy) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(extension,[status(thm),parent(t4:2)],[f_31_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(extension,[status(thm),parent(t2:3)],[f_29_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(extension,[status(thm),parent(t2:4)],[f_29_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:4]) ).
cnf(t12,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) != sdtasdt0(xz,xx)
| ~ sP26(sdtasdt0(xz,xl),sdtasdt0(xz,xk)) ),
inference(extension,[status(thm),parent(t1:2)],[f_33_9]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t1:2]) ).
cnf(t14,plain,
( sdtasdt0(xz,xx) != sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl))
| sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)) = sdtasdt0(xz,xx) ),
inference(extension,[status(thm),parent(t12:2)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(extension,[status(thm),parent(t14:2)],[f_32_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(extension,[status(thm),parent(t12:3)],[f_30_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:3]) ).
cnf(t20,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(extension,[status(thm),parent(t12:4)],[f_30_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t12:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG091+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
% 0.10/10.37 % Computer : n008.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Sat Sep 19 20:51:34 UTC 2026
% 0.10/10.37 % CPUTime :
% 190.13/200.49 % SZS status Theorem for theBenchmark
% 190.13/200.49 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------