%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU177+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 0.10s 0.45s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 231 ( 37 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 297 ( 113 ~; 104 |; 70 &)
% ( 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(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(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(f_24_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_24_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_24_1]) ).
fof(f_24_3,negated_conjecture,
? [U_27,U_26,U_25] :
( ( ~ in(U_26,relation_rng(U_25))
| ~ in(U_27,relation_dom(U_25)) )
& in(ordered_pair(U_27,U_26),U_25)
& relation(U_25) ),
inference(variable_rename,[status(thm)],[f_24_2]) ).
fof(f_24_4,negated_conjecture,
? [U_26,U_25] :
( ( ~ in(U_26,relation_rng(U_25))
| ~ in(sK5,relation_dom(U_25)) )
& in(ordered_pair(sK5,U_26),U_25)
& relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5)],[f_24_3]) ).
fof(f_24_5,negated_conjecture,
? [U_25] :
( ( ~ in(sK6,relation_rng(U_25))
| ~ in(sK5,relation_dom(U_25)) )
& in(ordered_pair(sK5,sK6),U_25)
& relation(U_25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_26,sK6)],[f_24_4]) ).
fof(f_24_6,negated_conjecture,
( ( ~ in(sK6,relation_rng(sK7))
| ~ in(sK5,relation_dom(sK7)) )
& in(ordered_pair(sK5,sK6),sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_25,sK7)],[f_24_5]) ).
fof(f_24_7,negated_conjecture,
( ( ~ in(sK6,relation_rng(sK7))
| ~ in(sK5,relation_dom(sK7)) )
& in(ordered_pair(sK5,sK6),sK7)
& relation(sK7) ),
inference(definitional_conversion,[status(esa)],[f_24_6]) ).
cnf(f_24_8,negated_conjecture,
relation(sK7),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_9,negated_conjecture,
in(ordered_pair(sK5,sK6),sK7),
inference(clausify,[status(thm)],[f_24_7]) ).
cnf(f_24_10,negated_conjecture,
( ~ in(sK6,relation_rng(sK7))
| ~ in(sK5,relation_dom(sK7)) ),
inference(clausify,[status(thm)],[f_24_7]) ).
fof(f_25_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_25_2,plain,
! [U_35] :
( ! [U_34] :
( ( U_34 = relation_dom(U_35)
| ? [U_33] :
( ( ~ in(U_33,U_34)
& ? [U_32] : in(ordered_pair(U_33,U_32),U_35) )
| ( ! [U_31] : ~ in(ordered_pair(U_33,U_31),U_35)
& in(U_33,U_34) ) ) )
& ( ! [U_30] :
( ( in(U_30,U_34)
| ! [U_29] : ~ in(ordered_pair(U_30,U_29),U_35) )
& ( ? [U_28] : in(ordered_pair(U_30,U_28),U_35)
| ~ in(U_30,U_34) ) )
| U_34 != relation_dom(U_35) ) )
| ~ relation(U_35) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_35] :
( ( ! [U_41] :
( U_41 = relation_dom(U_35)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] : in(ordered_pair(U_39,U_32),U_35) )
| ? [U_38] :
( ! [U_31] : ~ in(ordered_pair(U_38,U_31),U_35)
& in(U_38,U_41) ) )
& ! [U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] : ~ in(ordered_pair(U_37,U_29),U_35) )
& ! [U_36] :
( ? [U_28] : in(ordered_pair(U_36,U_28),U_35)
| ~ in(U_36,U_40) ) )
| U_40 != relation_dom(U_35) ) )
| ~ relation(U_35) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
! [U_35] :
( ( ! [U_41] :
( U_41 = relation_dom(U_35)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] : in(ordered_pair(U_39,U_32),U_35) )
| ? [U_38] :
( ! [U_31] : ~ in(ordered_pair(U_38,U_31),U_35)
& in(U_38,U_41) ) )
& ! [U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] : ~ in(ordered_pair(U_37,U_29),U_35) )
& ! [U_36] :
( in(ordered_pair(U_36,sK8(U_35,U_40,U_36)),U_35)
| ~ in(U_36,U_40) ) )
| U_40 != relation_dom(U_35) ) )
| ~ relation(U_35) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_28,sK8(U_35,U_40,U_36))],[f_25_3]) ).
fof(f_25_5,plain,
! [U_35] :
( ( ! [U_41] :
( U_41 = relation_dom(U_35)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] : in(ordered_pair(U_39,U_32),U_35) )
| ( ! [U_31] : ~ in(ordered_pair(sK9(U_35,U_41),U_31),U_35)
& in(sK9(U_35,U_41),U_41) ) )
& ! [U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] : ~ in(ordered_pair(U_37,U_29),U_35) )
& ! [U_36] :
( in(ordered_pair(U_36,sK8(U_35,U_40,U_36)),U_35)
| ~ in(U_36,U_40) ) )
| U_40 != relation_dom(U_35) ) )
| ~ relation(U_35) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_38,sK9(U_35,U_41))],[f_25_4]) ).
fof(f_25_6,plain,
! [U_35] :
( ( ! [U_41] :
( U_41 = relation_dom(U_35)
| ( ~ in(sK10(U_35,U_41),U_41)
& ? [U_32] : in(ordered_pair(sK10(U_35,U_41),U_32),U_35) )
| ( ! [U_31] : ~ in(ordered_pair(sK9(U_35,U_41),U_31),U_35)
& in(sK9(U_35,U_41),U_41) ) )
& ! [U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] : ~ in(ordered_pair(U_37,U_29),U_35) )
& ! [U_36] :
( in(ordered_pair(U_36,sK8(U_35,U_40,U_36)),U_35)
| ~ in(U_36,U_40) ) )
| U_40 != relation_dom(U_35) ) )
| ~ relation(U_35) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_39,sK10(U_35,U_41))],[f_25_5]) ).
fof(f_25_7,plain,
! [U_35] :
( ( ! [U_41] :
( U_41 = relation_dom(U_35)
| ( ~ in(sK10(U_35,U_41),U_41)
& in(ordered_pair(sK10(U_35,U_41),sK11(U_35,U_41)),U_35) )
| ( ! [U_31] : ~ in(ordered_pair(sK9(U_35,U_41),U_31),U_35)
& in(sK9(U_35,U_41),U_41) ) )
& ! [U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] : ~ in(ordered_pair(U_37,U_29),U_35) )
& ! [U_36] :
( in(ordered_pair(U_36,sK8(U_35,U_40,U_36)),U_35)
| ~ in(U_36,U_40) ) )
| U_40 != relation_dom(U_35) ) )
| ~ relation(U_35) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_32,sK11(U_35,U_41))],[f_25_6]) ).
cnf(f_25_9,plain,
( in(U_37,U_40)
| ~ in(ordered_pair(U_37,U_29),U_35)
| U_40 != relation_dom(U_35)
| ~ relation(U_35) ),
inference(clausify,[status(thm)],[f_25_7]) ).
fof(f_26_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_26_2,plain,
! [U_49] :
( ! [U_48] :
( ( U_48 = relation_rng(U_49)
| ? [U_47] :
( ( ~ in(U_47,U_48)
& ? [U_46] : in(ordered_pair(U_46,U_47),U_49) )
| ( ! [U_45] : ~ in(ordered_pair(U_45,U_47),U_49)
& in(U_47,U_48) ) ) )
& ( ! [U_44] :
( ( in(U_44,U_48)
| ! [U_43] : ~ in(ordered_pair(U_43,U_44),U_49) )
& ( ? [U_42] : in(ordered_pair(U_42,U_44),U_49)
| ~ in(U_44,U_48) ) )
| U_48 != relation_rng(U_49) ) )
| ~ relation(U_49) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_49] :
( ( ! [U_55] :
( U_55 = relation_rng(U_49)
| ? [U_53] :
( ~ in(U_53,U_55)
& ? [U_46] : in(ordered_pair(U_46,U_53),U_49) )
| ? [U_52] :
( ! [U_45] : ~ in(ordered_pair(U_45,U_52),U_49)
& in(U_52,U_55) ) )
& ! [U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ! [U_43] : ~ in(ordered_pair(U_43,U_51),U_49) )
& ! [U_50] :
( ? [U_42] : in(ordered_pair(U_42,U_50),U_49)
| ~ in(U_50,U_54) ) )
| U_54 != relation_rng(U_49) ) )
| ~ relation(U_49) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_49] :
( ( ! [U_55] :
( U_55 = relation_rng(U_49)
| ? [U_53] :
( ~ in(U_53,U_55)
& ? [U_46] : in(ordered_pair(U_46,U_53),U_49) )
| ? [U_52] :
( ! [U_45] : ~ in(ordered_pair(U_45,U_52),U_49)
& in(U_52,U_55) ) )
& ! [U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ! [U_43] : ~ in(ordered_pair(U_43,U_51),U_49) )
& ! [U_50] :
( in(ordered_pair(sK12(U_49,U_54,U_50),U_50),U_49)
| ~ in(U_50,U_54) ) )
| U_54 != relation_rng(U_49) ) )
| ~ relation(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_42,sK12(U_49,U_54,U_50))],[f_26_3]) ).
fof(f_26_5,plain,
! [U_49] :
( ( ! [U_55] :
( U_55 = relation_rng(U_49)
| ? [U_53] :
( ~ in(U_53,U_55)
& ? [U_46] : in(ordered_pair(U_46,U_53),U_49) )
| ( ! [U_45] : ~ in(ordered_pair(U_45,sK13(U_49,U_55)),U_49)
& in(sK13(U_49,U_55),U_55) ) )
& ! [U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ! [U_43] : ~ in(ordered_pair(U_43,U_51),U_49) )
& ! [U_50] :
( in(ordered_pair(sK12(U_49,U_54,U_50),U_50),U_49)
| ~ in(U_50,U_54) ) )
| U_54 != relation_rng(U_49) ) )
| ~ relation(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_52,sK13(U_49,U_55))],[f_26_4]) ).
fof(f_26_6,plain,
! [U_49] :
( ( ! [U_55] :
( U_55 = relation_rng(U_49)
| ( ~ in(sK14(U_49,U_55),U_55)
& ? [U_46] : in(ordered_pair(U_46,sK14(U_49,U_55)),U_49) )
| ( ! [U_45] : ~ in(ordered_pair(U_45,sK13(U_49,U_55)),U_49)
& in(sK13(U_49,U_55),U_55) ) )
& ! [U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ! [U_43] : ~ in(ordered_pair(U_43,U_51),U_49) )
& ! [U_50] :
( in(ordered_pair(sK12(U_49,U_54,U_50),U_50),U_49)
| ~ in(U_50,U_54) ) )
| U_54 != relation_rng(U_49) ) )
| ~ relation(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_53,sK14(U_49,U_55))],[f_26_5]) ).
fof(f_26_7,plain,
! [U_49] :
( ( ! [U_55] :
( U_55 = relation_rng(U_49)
| ( ~ in(sK14(U_49,U_55),U_55)
& in(ordered_pair(sK15(U_49,U_55),sK14(U_49,U_55)),U_49) )
| ( ! [U_45] : ~ in(ordered_pair(U_45,sK13(U_49,U_55)),U_49)
& in(sK13(U_49,U_55),U_55) ) )
& ! [U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| ! [U_43] : ~ in(ordered_pair(U_43,U_51),U_49) )
& ! [U_50] :
( in(ordered_pair(sK12(U_49,U_54,U_50),U_50),U_49)
| ~ in(U_50,U_54) ) )
| U_54 != relation_rng(U_49) ) )
| ~ relation(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_46,sK15(U_49,U_55))],[f_26_6]) ).
cnf(f_26_9,plain,
( in(U_51,U_54)
| ~ in(ordered_pair(U_43,U_51),U_49)
| U_54 != relation_rng(U_49)
| ~ relation(U_49) ),
inference(clausify,[status(thm)],[f_26_7]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( ~ in(sK6,relation_rng(sK7))
| ~ in(sK5,relation_dom(sK7)) ),
inference(start,[status(thm),parent(0:0)],[f_24_10]) ).
cnf(t2,plain,
( relation_dom(sK7) != relation_dom(sK7)
| ~ in(ordered_pair(sK5,sK6),sK7)
| ~ relation(sK7)
| in(sK5,relation_dom(sK7)) ),
inference(extension,[status(thm),parent(t1:1)],[f_25_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
relation(sK7),
inference(extension,[status(thm),parent(t2:2)],[f_24_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
in(ordered_pair(sK5,sK6),sK7),
inference(extension,[status(thm),parent(t2:3)],[f_24_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
relation_dom(sK7) = relation_dom(sK7),
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(sK7) != relation_rng(sK7)
| ~ in(ordered_pair(sK5,sK6),sK7)
| ~ relation(sK7)
| in(sK6,relation_rng(sK7)) ),
inference(extension,[status(thm),parent(t1:2)],[f_26_9]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
relation(sK7),
inference(extension,[status(thm),parent(t10:2)],[f_24_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
in(ordered_pair(sK5,sK6),sK7),
inference(extension,[status(thm),parent(t10:3)],[f_24_9]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
relation_rng(sK7) = relation_rng(sK7),
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+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:26:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------