%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU177+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 : 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 08:58:22 AM UTC 2026
% Result : Theorem 76.64s 76.99s
% Output : Proof 76.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 17 unt; 0 def)
% Number of atoms : 227 ( 37 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 292 ( 111 ~; 103 |; 68 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 154 ( 2 sgn 102 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(t20_relat_1,conjecture,
! [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(f_17_1,plain,
! [A] :
( ! [B] :
( ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(C,D),A) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_relat_1]) ).
fof(f_17_2,plain,
! [U_158] :
( ! [U_157] :
( ( U_157 = relation_dom(U_158)
| ? [U_156] :
( ( ~ in(U_156,U_157)
& ? [U_155] : in(ordered_pair(U_156,U_155),U_158) )
| ( ! [U_154] : ~ in(ordered_pair(U_156,U_154),U_158)
& in(U_156,U_157) ) ) )
& ( ! [U_153] :
( ( in(U_153,U_157)
| ! [U_152] : ~ in(ordered_pair(U_153,U_152),U_158) )
& ( ? [U_151] : in(ordered_pair(U_153,U_151),U_158)
| ~ in(U_153,U_157) ) )
| U_157 != relation_dom(U_158) ) )
| ~ relation(U_158) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_158] :
( ( ! [U_164] :
( U_164 = relation_dom(U_158)
| ? [U_162] :
( ~ in(U_162,U_164)
& ? [U_155] : in(ordered_pair(U_162,U_155),U_158) )
| ? [U_161] :
( ! [U_154] : ~ in(ordered_pair(U_161,U_154),U_158)
& in(U_161,U_164) ) )
& ! [U_163] :
( ( ! [U_160] :
( in(U_160,U_163)
| ! [U_152] : ~ in(ordered_pair(U_160,U_152),U_158) )
& ! [U_159] :
( ? [U_151] : in(ordered_pair(U_159,U_151),U_158)
| ~ in(U_159,U_163) ) )
| U_163 != relation_dom(U_158) ) )
| ~ relation(U_158) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
! [U_158] :
( ( ! [U_164] :
( U_164 = relation_dom(U_158)
| ? [U_162] :
( ~ in(U_162,U_164)
& ? [U_155] : in(ordered_pair(U_162,U_155),U_158) )
| ? [U_161] :
( ! [U_154] : ~ in(ordered_pair(U_161,U_154),U_158)
& in(U_161,U_164) ) )
& ! [U_163] :
( ( ! [U_160] :
( in(U_160,U_163)
| ! [U_152] : ~ in(ordered_pair(U_160,U_152),U_158) )
& ! [U_159] :
( in(ordered_pair(U_159,sK23(U_158,U_163,U_159)),U_158)
| ~ in(U_159,U_163) ) )
| U_163 != relation_dom(U_158) ) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_151,sK23(U_158,U_163,U_159))],[f_17_3]) ).
fof(f_17_5,plain,
! [U_158] :
( ( ! [U_164] :
( U_164 = relation_dom(U_158)
| ? [U_162] :
( ~ in(U_162,U_164)
& ? [U_155] : in(ordered_pair(U_162,U_155),U_158) )
| ( ! [U_154] : ~ in(ordered_pair(sK24(U_158,U_164),U_154),U_158)
& in(sK24(U_158,U_164),U_164) ) )
& ! [U_163] :
( ( ! [U_160] :
( in(U_160,U_163)
| ! [U_152] : ~ in(ordered_pair(U_160,U_152),U_158) )
& ! [U_159] :
( in(ordered_pair(U_159,sK23(U_158,U_163,U_159)),U_158)
| ~ in(U_159,U_163) ) )
| U_163 != relation_dom(U_158) ) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_161,sK24(U_158,U_164))],[f_17_4]) ).
fof(f_17_6,plain,
! [U_158] :
( ( ! [U_164] :
( U_164 = relation_dom(U_158)
| ( ~ in(sK25(U_158,U_164),U_164)
& ? [U_155] : in(ordered_pair(sK25(U_158,U_164),U_155),U_158) )
| ( ! [U_154] : ~ in(ordered_pair(sK24(U_158,U_164),U_154),U_158)
& in(sK24(U_158,U_164),U_164) ) )
& ! [U_163] :
( ( ! [U_160] :
( in(U_160,U_163)
| ! [U_152] : ~ in(ordered_pair(U_160,U_152),U_158) )
& ! [U_159] :
( in(ordered_pair(U_159,sK23(U_158,U_163,U_159)),U_158)
| ~ in(U_159,U_163) ) )
| U_163 != relation_dom(U_158) ) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_162,sK25(U_158,U_164))],[f_17_5]) ).
fof(f_17_7,plain,
! [U_158] :
( ( ! [U_164] :
( U_164 = relation_dom(U_158)
| ( ~ in(sK25(U_158,U_164),U_164)
& in(ordered_pair(sK25(U_158,U_164),sK26(U_158,U_164)),U_158) )
| ( ! [U_154] : ~ in(ordered_pair(sK24(U_158,U_164),U_154),U_158)
& in(sK24(U_158,U_164),U_164) ) )
& ! [U_163] :
( ( ! [U_160] :
( in(U_160,U_163)
| ! [U_152] : ~ in(ordered_pair(U_160,U_152),U_158) )
& ! [U_159] :
( in(ordered_pair(U_159,sK23(U_158,U_163,U_159)),U_158)
| ~ in(U_159,U_163) ) )
| U_163 != relation_dom(U_158) ) )
| ~ relation(U_158) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_155,sK26(U_158,U_164))],[f_17_6]) ).
cnf(f_17_9,plain,
( in(U_160,U_163)
| ~ in(ordered_pair(U_160,U_152),U_158)
| U_163 != relation_dom(U_158)
| ~ relation(U_158) ),
inference(clausify,[status(thm)],[f_17_7]) ).
fof(f_21_1,plain,
! [A] :
( ! [B] :
( ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] : in(ordered_pair(D,C),A) )
| ( ! [D] : ~ in(ordered_pair(D,C),A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d5_relat_1]) ).
fof(f_21_2,plain,
! [U_204] :
( ! [U_203] :
( ( U_203 = relation_rng(U_204)
| ? [U_202] :
( ( ~ in(U_202,U_203)
& ? [U_201] : in(ordered_pair(U_201,U_202),U_204) )
| ( ! [U_200] : ~ in(ordered_pair(U_200,U_202),U_204)
& in(U_202,U_203) ) ) )
& ( ! [U_199] :
( ( in(U_199,U_203)
| ! [U_198] : ~ in(ordered_pair(U_198,U_199),U_204) )
& ( ? [U_197] : in(ordered_pair(U_197,U_199),U_204)
| ~ in(U_199,U_203) ) )
| U_203 != relation_rng(U_204) ) )
| ~ relation(U_204) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_204] :
( ( ! [U_210] :
( U_210 = relation_rng(U_204)
| ? [U_208] :
( ~ in(U_208,U_210)
& ? [U_201] : in(ordered_pair(U_201,U_208),U_204) )
| ? [U_207] :
( ! [U_200] : ~ in(ordered_pair(U_200,U_207),U_204)
& in(U_207,U_210) ) )
& ! [U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| ! [U_198] : ~ in(ordered_pair(U_198,U_206),U_204) )
& ! [U_205] :
( ? [U_197] : in(ordered_pair(U_197,U_205),U_204)
| ~ in(U_205,U_209) ) )
| U_209 != relation_rng(U_204) ) )
| ~ relation(U_204) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
! [U_204] :
( ( ! [U_210] :
( U_210 = relation_rng(U_204)
| ? [U_208] :
( ~ in(U_208,U_210)
& ? [U_201] : in(ordered_pair(U_201,U_208),U_204) )
| ? [U_207] :
( ! [U_200] : ~ in(ordered_pair(U_200,U_207),U_204)
& in(U_207,U_210) ) )
& ! [U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| ! [U_198] : ~ in(ordered_pair(U_198,U_206),U_204) )
& ! [U_205] :
( in(ordered_pair(sK33(U_204,U_209,U_205),U_205),U_204)
| ~ in(U_205,U_209) ) )
| U_209 != relation_rng(U_204) ) )
| ~ relation(U_204) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_197,sK33(U_204,U_209,U_205))],[f_21_3]) ).
fof(f_21_5,plain,
! [U_204] :
( ( ! [U_210] :
( U_210 = relation_rng(U_204)
| ? [U_208] :
( ~ in(U_208,U_210)
& ? [U_201] : in(ordered_pair(U_201,U_208),U_204) )
| ( ! [U_200] : ~ in(ordered_pair(U_200,sK34(U_204,U_210)),U_204)
& in(sK34(U_204,U_210),U_210) ) )
& ! [U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| ! [U_198] : ~ in(ordered_pair(U_198,U_206),U_204) )
& ! [U_205] :
( in(ordered_pair(sK33(U_204,U_209,U_205),U_205),U_204)
| ~ in(U_205,U_209) ) )
| U_209 != relation_rng(U_204) ) )
| ~ relation(U_204) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_207,sK34(U_204,U_210))],[f_21_4]) ).
fof(f_21_6,plain,
! [U_204] :
( ( ! [U_210] :
( U_210 = relation_rng(U_204)
| ( ~ in(sK35(U_204,U_210),U_210)
& ? [U_201] : in(ordered_pair(U_201,sK35(U_204,U_210)),U_204) )
| ( ! [U_200] : ~ in(ordered_pair(U_200,sK34(U_204,U_210)),U_204)
& in(sK34(U_204,U_210),U_210) ) )
& ! [U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| ! [U_198] : ~ in(ordered_pair(U_198,U_206),U_204) )
& ! [U_205] :
( in(ordered_pair(sK33(U_204,U_209,U_205),U_205),U_204)
| ~ in(U_205,U_209) ) )
| U_209 != relation_rng(U_204) ) )
| ~ relation(U_204) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_208,sK35(U_204,U_210))],[f_21_5]) ).
fof(f_21_7,plain,
! [U_204] :
( ( ! [U_210] :
( U_210 = relation_rng(U_204)
| ( ~ in(sK35(U_204,U_210),U_210)
& in(ordered_pair(sK36(U_204,U_210),sK35(U_204,U_210)),U_204) )
| ( ! [U_200] : ~ in(ordered_pair(U_200,sK34(U_204,U_210)),U_204)
& in(sK34(U_204,U_210),U_210) ) )
& ! [U_209] :
( ( ! [U_206] :
( in(U_206,U_209)
| ! [U_198] : ~ in(ordered_pair(U_198,U_206),U_204) )
& ! [U_205] :
( in(ordered_pair(sK33(U_204,U_209,U_205),U_205),U_204)
| ~ in(U_205,U_209) ) )
| U_209 != relation_rng(U_204) ) )
| ~ relation(U_204) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_201,sK36(U_204,U_210))],[f_21_6]) ).
cnf(f_21_9,plain,
( in(U_206,U_209)
| ~ in(ordered_pair(U_198,U_206),U_204)
| U_209 != relation_rng(U_204)
| ~ relation(U_204) ),
inference(clausify,[status(thm)],[f_21_7]) ).
fof(f_94_1,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
inference(negate,[status(cth)],[t20_relat_1]) ).
fof(f_94_2,negated_conjecture,
? [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)],[f_94_1]) ).
fof(f_94_3,negated_conjecture,
? [U_378,U_377,U_376] :
( ( ~ in(U_377,relation_rng(U_376))
| ~ in(U_378,relation_dom(U_376)) )
& in(ordered_pair(U_378,U_377),U_376)
& relation(U_376) ),
inference(variable_rename,[status(thm)],[f_94_2]) ).
fof(f_94_4,negated_conjecture,
? [U_377,U_376] :
( ( ~ in(U_377,relation_rng(U_376))
| ~ in(sK46,relation_dom(U_376)) )
& in(ordered_pair(sK46,U_377),U_376)
& relation(U_376) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_378,sK46)],[f_94_3]) ).
fof(f_94_5,negated_conjecture,
? [U_376] :
( ( ~ in(sK47,relation_rng(U_376))
| ~ in(sK46,relation_dom(U_376)) )
& in(ordered_pair(sK46,sK47),U_376)
& relation(U_376) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_377,sK47)],[f_94_4]) ).
fof(f_94_6,negated_conjecture,
( ( ~ in(sK47,relation_rng(sK48))
| ~ in(sK46,relation_dom(sK48)) )
& in(ordered_pair(sK46,sK47),sK48)
& relation(sK48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_376,sK48)],[f_94_5]) ).
cnf(f_94_7,negated_conjecture,
relation(sK48),
inference(clausify,[status(thm)],[f_94_6]) ).
cnf(f_94_8,negated_conjecture,
in(ordered_pair(sK46,sK47),sK48),
inference(clausify,[status(thm)],[f_94_6]) ).
cnf(f_94_9,negated_conjecture,
( ~ in(sK47,relation_rng(sK48))
| ~ in(sK46,relation_dom(sK48)) ),
inference(clausify,[status(thm)],[f_94_6]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( ~ in(sK47,relation_rng(sK48))
| ~ in(sK46,relation_dom(sK48)) ),
inference(start,[status(thm),parent(0:0)],[f_94_9]) ).
cnf(t2,plain,
( relation_dom(sK48) != relation_dom(sK48)
| ~ in(ordered_pair(sK46,sK47),sK48)
| ~ relation(sK48)
| in(sK46,relation_dom(sK48)) ),
inference(extension,[status(thm),parent(t1:1)],[f_17_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
relation(sK48),
inference(extension,[status(thm),parent(t2:2)],[f_94_7]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
in(ordered_pair(sK46,sK47),sK48),
inference(extension,[status(thm),parent(t2:3)],[f_94_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
relation_dom(sK48) = relation_dom(sK48),
inference(extension,[status(thm),parent(t2:4)],[equality_1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
( relation_rng(sK48) != relation_rng(sK48)
| ~ in(ordered_pair(sK46,sK47),sK48)
| ~ relation(sK48)
| in(sK47,relation_rng(sK48)) ),
inference(extension,[status(thm),parent(t1:2)],[f_21_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
relation(sK48),
inference(extension,[status(thm),parent(t10:2)],[f_94_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
in(ordered_pair(sK46,sK47),sK48),
inference(extension,[status(thm),parent(t10:3)],[f_94_8]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
relation_rng(sK48) = relation_rng(sK48),
inference(extension,[status(thm),parent(t10:4)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU177+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
% 0.07/0.36 % Computer : n008.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 23:26:55 UTC 2026
% 0.07/0.36 % CPUTime :
% 76.64/76.99 % SZS status Theorem for theBenchmark
% 76.64/76.99 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------