%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n007.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 08:58:31 AM UTC 2026
% Result : Theorem 83.65s 84.00s
% Output : Proof 83.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 27 unt; 0 def)
% Number of atoms : 173 ( 41 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 188 ( 68 ~; 66 |; 43 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 1 sgn 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('theBenchmark.p',d4_funct_1) ).
fof(t20_relat_1,lemma,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t20_relat_1) ).
fof(t8_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('theBenchmark.p',t8_funct_1) ).
fof(f_27_1,plain,
! [A] :
( ! [B,C] :
( ( ( ( C = apply(A,B)
| C != empty_set )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_funct_1]) ).
fof(f_27_2,plain,
! [U_262] :
( ! [U_261,U_260] :
( ( ( ( U_260 = apply(U_262,U_261)
| U_260 != empty_set )
& ( U_260 = empty_set
| U_260 != apply(U_262,U_261) ) )
| in(U_261,relation_dom(U_262)) )
& ( ( ( U_260 = apply(U_262,U_261)
| ~ in(ordered_pair(U_261,U_260),U_262) )
& ( in(ordered_pair(U_261,U_260),U_262)
| U_260 != apply(U_262,U_261) ) )
| ~ in(U_261,relation_dom(U_262)) ) )
| ~ function(U_262)
| ~ relation(U_262) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_262] :
( ( ! [U_270] :
( ( ! [U_268] :
( U_268 = apply(U_262,U_270)
| U_268 != empty_set )
& ! [U_267] :
( U_267 = empty_set
| U_267 != apply(U_262,U_270) ) )
| in(U_270,relation_dom(U_262)) )
& ! [U_269] :
( ( ! [U_266] :
( U_266 = apply(U_262,U_269)
| ~ in(ordered_pair(U_269,U_266),U_262) )
& ! [U_265] :
( in(ordered_pair(U_269,U_265),U_262)
| U_265 != apply(U_262,U_269) ) )
| ~ in(U_269,relation_dom(U_262)) ) )
| ~ function(U_262)
| ~ relation(U_262) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( in(ordered_pair(U_269,U_265),U_262)
| U_265 != apply(U_262,U_269)
| ~ in(U_269,relation_dom(U_262))
| ~ function(U_262)
| ~ relation(U_262) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( U_266 = apply(U_262,U_269)
| ~ in(ordered_pair(U_269,U_266),U_262)
| ~ in(U_269,relation_dom(U_262))
| ~ function(U_262)
| ~ relation(U_262) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_147_1,plain,
! [A,B,C] :
( ( in(B,relation_rng(C))
& in(A,relation_dom(C)) )
| ~ in(ordered_pair(A,B),C)
| ~ relation(C) ),
inference(fof_nnf,[status(thm)],[t20_relat_1]) ).
fof(f_147_2,plain,
! [U_596,U_595,U_594] :
( ( in(U_595,relation_rng(U_594))
& in(U_596,relation_dom(U_594)) )
| ~ in(ordered_pair(U_596,U_595),U_594)
| ~ relation(U_594) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( in(U_596,relation_dom(U_594))
| ~ in(ordered_pair(U_596,U_595),U_594)
| ~ relation(U_594) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_206_1,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[t8_funct_1]) ).
fof(f_206_2,negated_conjecture,
? [A,B,C] :
( ( ( ~ in(ordered_pair(A,B),C)
& B = apply(C,A)
& in(A,relation_dom(C)) )
| ( ( B != apply(C,A)
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C) ) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[f_206_1]) ).
fof(f_206_3,negated_conjecture,
? [U_764,U_763,U_762] :
( ( ( ~ in(ordered_pair(U_764,U_763),U_762)
& U_763 = apply(U_762,U_764)
& in(U_764,relation_dom(U_762)) )
| ( ( U_763 != apply(U_762,U_764)
| ~ in(U_764,relation_dom(U_762)) )
& in(ordered_pair(U_764,U_763),U_762) ) )
& function(U_762)
& relation(U_762) ),
inference(variable_rename,[status(thm)],[f_206_2]) ).
fof(f_206_4,negated_conjecture,
? [U_763,U_762] :
( ( ( ~ in(ordered_pair(sK96,U_763),U_762)
& U_763 = apply(U_762,sK96)
& in(sK96,relation_dom(U_762)) )
| ( ( U_763 != apply(U_762,sK96)
| ~ in(sK96,relation_dom(U_762)) )
& in(ordered_pair(sK96,U_763),U_762) ) )
& function(U_762)
& relation(U_762) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_764,sK96)],[f_206_3]) ).
fof(f_206_5,negated_conjecture,
? [U_762] :
( ( ( ~ in(ordered_pair(sK96,sK97),U_762)
& sK97 = apply(U_762,sK96)
& in(sK96,relation_dom(U_762)) )
| ( ( sK97 != apply(U_762,sK96)
| ~ in(sK96,relation_dom(U_762)) )
& in(ordered_pair(sK96,sK97),U_762) ) )
& function(U_762)
& relation(U_762) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_763,sK97)],[f_206_4]) ).
fof(f_206_6,negated_conjecture,
( ( ( ~ in(ordered_pair(sK96,sK97),sK98)
& sK97 = apply(sK98,sK96)
& in(sK96,relation_dom(sK98)) )
| ( ( sK97 != apply(sK98,sK96)
| ~ in(sK96,relation_dom(sK98)) )
& in(ordered_pair(sK96,sK97),sK98) ) )
& function(sK98)
& relation(sK98) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_762,sK98)],[f_206_5]) ).
cnf(f_206_7,negated_conjecture,
relation(sK98),
inference(clausify,[status(thm)],[f_206_6]) ).
cnf(f_206_8,negated_conjecture,
function(sK98),
inference(clausify,[status(thm)],[f_206_6]) ).
cnf(f_206_9,negated_conjecture,
( in(sK96,relation_dom(sK98))
| in(ordered_pair(sK96,sK97),sK98) ),
inference(clausify,[status(thm)],[f_206_6]) ).
cnf(f_206_10,negated_conjecture,
( sK97 = apply(sK98,sK96)
| in(ordered_pair(sK96,sK97),sK98) ),
inference(clausify,[status(thm)],[f_206_6]) ).
cnf(f_206_14,negated_conjecture,
( ~ in(ordered_pair(sK96,sK97),sK98)
| sK97 != apply(sK98,sK96)
| ~ in(sK96,relation_dom(sK98)) ),
inference(clausify,[status(thm)],[f_206_6]) ).
cnf(t1,plain,
( sK97 != apply(sK98,sK96)
| ~ in(ordered_pair(sK96,sK97),sK98)
| ~ in(sK96,relation_dom(sK98)) ),
inference(start,[status(thm),parent(0:0)],[f_206_14]) ).
cnf(t2,plain,
( ~ in(ordered_pair(sK96,sK97),sK98)
| ~ relation(sK98)
| in(sK96,relation_dom(sK98)) ),
inference(extension,[status(thm),parent(t1:1)],[f_147_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
relation(sK98),
inference(extension,[status(thm),parent(t2:2)],[f_206_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( in(sK96,relation_dom(sK98))
| in(ordered_pair(sK96,sK97),sK98) ),
inference(extension,[status(thm),parent(t2:3)],[f_206_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
$false,
inference(reduction,[status(thm),parent(t6:2)],[t6:2,t1:1]) ).
cnf(l1,lemma,
in(sK96,relation_dom(sK98)),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t9,plain,
( ~ function(sK98)
| ~ in(sK96,relation_dom(sK98))
| sK97 != apply(sK98,sK96)
| ~ relation(sK98)
| in(ordered_pair(sK96,sK97),sK98) ),
inference(extension,[status(thm),parent(t1:2)],[f_27_4]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t1:2]) ).
cnf(t11,plain,
relation(sK98),
inference(extension,[status(thm),parent(t9:2)],[f_206_7]) ).
cnf(t12,plain,
$false,
inference(connection,[status(thm),parent(t11:1)],[t11:1,t9:2]) ).
cnf(t13,plain,
( in(ordered_pair(sK96,sK97),sK98)
| sK97 = apply(sK98,sK96) ),
inference(extension,[status(thm),parent(t9:3)],[f_206_10]) ).
cnf(t14,plain,
$false,
inference(connection,[status(thm),parent(t13:1)],[t13:1,t9:3]) ).
cnf(t15,plain,
$false,
inference(reduction,[status(thm),parent(t13:2)],[t13:2,t1:2]) ).
cnf(t16,plain,
in(sK96,relation_dom(sK98)),
inference(lemma_extension,[status(thm),parent(t9:4)],[l1:1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t9:4]) ).
cnf(t18,plain,
function(sK98),
inference(extension,[status(thm),parent(t9:5)],[f_206_8]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t9:5]) ).
cnf(l5,lemma,
in(ordered_pair(sK96,sK97),sK98),
inference(lemma,[status(cth),parent(t1:2),below(0:0)],[t1:2]) ).
cnf(t20,plain,
( ~ function(sK98)
| ~ in(sK96,relation_dom(sK98))
| ~ in(ordered_pair(sK96,sK97),sK98)
| ~ relation(sK98)
| sK97 = apply(sK98,sK96) ),
inference(extension,[status(thm),parent(t1:3)],[f_27_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t1:3]) ).
cnf(t22,plain,
relation(sK98),
inference(extension,[status(thm),parent(t20:2)],[f_206_7]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
in(ordered_pair(sK96,sK97),sK98),
inference(lemma_extension,[status(thm),parent(t20:3)],[l5:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
in(sK96,relation_dom(sK98)),
inference(lemma_extension,[status(thm),parent(t20:4)],[l1:1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t20:4]) ).
cnf(t28,plain,
function(sK98),
inference(extension,[status(thm),parent(t20:5)],[f_206_8]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t20:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU212+2 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:29:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 83.65/84.00 % SZS status Theorem for theBenchmark
% 83.65/84.00 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------