%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU267+1 : 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 : n018.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 08:58:47 AM UTC 2026
% Result : Theorem 0.10s 0.42s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 15 unt; 0 def)
% Number of atoms : 133 ( 125 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 163 ( 73 ~; 62 |; 22 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 123 ( 6 sgn 78 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t7_mcart_1,conjecture,
! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
file('theBenchmark.p',t7_mcart_1) ).
fof(d1_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_first(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = C ) ) ),
file('theBenchmark.p',d1_mcart_1) ).
fof(d2_mcart_1,axiom,
! [A] :
( ? [B,C] : A = ordered_pair(B,C)
=> ! [B] :
( B = pair_second(A)
<=> ! [C,D] :
( A = ordered_pair(C,D)
=> B = D ) ) ),
file('theBenchmark.p',d2_mcart_1) ).
fof(f_17_1,negated_conjecture,
~ ! [A,B] :
( pair_second(ordered_pair(A,B)) = B
& pair_first(ordered_pair(A,B)) = A ),
inference(negate,[status(cth)],[t7_mcart_1]) ).
fof(f_17_2,negated_conjecture,
? [A,B] :
( pair_second(ordered_pair(A,B)) != B
| pair_first(ordered_pair(A,B)) != A ),
inference(fof_nnf,[status(thm)],[f_17_1]) ).
fof(f_17_3,negated_conjecture,
? [U_18,U_17] :
( pair_second(ordered_pair(U_18,U_17)) != U_17
| pair_first(ordered_pair(U_18,U_17)) != U_18 ),
inference(variable_rename,[status(thm)],[f_17_2]) ).
fof(f_17_4,negated_conjecture,
( ? [U_22,U_20] : pair_second(ordered_pair(U_22,U_20)) != U_20
| ? [U_21,U_19] : pair_first(ordered_pair(U_21,U_19)) != U_21 ),
inference(miniscope,[status(thm)],[f_17_3]) ).
fof(f_17_5,negated_conjecture,
( ? [U_22,U_20] : pair_second(ordered_pair(U_22,U_20)) != U_20
| ? [U_19] : pair_first(ordered_pair(sK4,U_19)) != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4)],[f_17_4]) ).
fof(f_17_6,negated_conjecture,
( ? [U_22,U_20] : pair_second(ordered_pair(U_22,U_20)) != U_20
| pair_first(ordered_pair(sK4,sK5)) != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_19,sK5)],[f_17_5]) ).
fof(f_17_7,negated_conjecture,
( ? [U_20] : pair_second(ordered_pair(sK6,U_20)) != U_20
| pair_first(ordered_pair(sK4,sK5)) != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_17_6]) ).
fof(f_17_8,negated_conjecture,
( pair_second(ordered_pair(sK6,sK7)) != sK7
| pair_first(ordered_pair(sK4,sK5)) != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_20,sK7)],[f_17_7]) ).
fof(f_17_9,negated_conjecture,
( pair_second(ordered_pair(sK6,sK7)) != sK7
| pair_first(ordered_pair(sK4,sK5)) != sK4 ),
inference(definitional_conversion,[status(esa)],[f_17_8]) ).
cnf(f_17_10,negated_conjecture,
( pair_second(ordered_pair(sK6,sK7)) != sK7
| pair_first(ordered_pair(sK4,sK5)) != sK4 ),
inference(clausify,[status(thm)],[f_17_9]) ).
fof(f_18_1,plain,
! [A] :
( ! [B] :
( ( B = pair_first(A)
| ? [C,D] :
( B != C
& A = ordered_pair(C,D) ) )
& ( ! [C,D] :
( B = C
| A != ordered_pair(C,D) )
| B != pair_first(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[d1_mcart_1]) ).
fof(f_18_2,plain,
! [U_30] :
( ! [U_29] :
( ( U_29 = pair_first(U_30)
| ? [U_28,U_27] :
( U_29 != U_28
& U_30 = ordered_pair(U_28,U_27) ) )
& ( ! [U_26,U_25] :
( U_29 = U_26
| U_30 != ordered_pair(U_26,U_25) )
| U_29 != pair_first(U_30) ) )
| ! [U_24,U_23] : U_30 != ordered_pair(U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_30] :
( ( ! [U_32] :
( U_32 = pair_first(U_30)
| ? [U_28] :
( ? [U_27] : U_30 = ordered_pair(U_28,U_27)
& U_32 != U_28 ) )
& ! [U_31] :
( ! [U_26] :
( ! [U_25] : U_30 != ordered_pair(U_26,U_25)
| U_31 = U_26 )
| U_31 != pair_first(U_30) ) )
| ! [U_24,U_23] : U_30 != ordered_pair(U_24,U_23) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
! [U_30] :
( ( ! [U_32] :
( U_32 = pair_first(U_30)
| ( ? [U_27] : U_30 = ordered_pair(sK8(U_30,U_32),U_27)
& U_32 != sK8(U_30,U_32) ) )
& ! [U_31] :
( ! [U_26] :
( ! [U_25] : U_30 != ordered_pair(U_26,U_25)
| U_31 = U_26 )
| U_31 != pair_first(U_30) ) )
| ! [U_24,U_23] : U_30 != ordered_pair(U_24,U_23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_28,sK8(U_30,U_32))],[f_18_3]) ).
fof(f_18_5,plain,
! [U_30] :
( ( ! [U_32] :
( U_32 = pair_first(U_30)
| ( U_30 = ordered_pair(sK8(U_30,U_32),sK9(U_30,U_32))
& U_32 != sK8(U_30,U_32) ) )
& ! [U_31] :
( ! [U_26] :
( ! [U_25] : U_30 != ordered_pair(U_26,U_25)
| U_31 = U_26 )
| U_31 != pair_first(U_30) ) )
| ! [U_24,U_23] : U_30 != ordered_pair(U_24,U_23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9(U_30,U_32))],[f_18_4]) ).
cnf(f_18_6,plain,
( U_30 != ordered_pair(U_26,U_25)
| U_31 = U_26
| U_31 != pair_first(U_30)
| U_30 != ordered_pair(U_24,U_23) ),
inference(clausify,[status(thm)],[f_18_5]) ).
fof(f_19_1,plain,
! [A] :
( ! [B] :
( ( B = pair_second(A)
| ? [C,D] :
( B != D
& A = ordered_pair(C,D) ) )
& ( ! [C,D] :
( B = D
| A != ordered_pair(C,D) )
| B != pair_second(A) ) )
| ! [B,C] : A != ordered_pair(B,C) ),
inference(fof_nnf,[status(thm)],[d2_mcart_1]) ).
fof(f_19_2,plain,
! [U_40] :
( ! [U_39] :
( ( U_39 = pair_second(U_40)
| ? [U_38,U_37] :
( U_39 != U_37
& U_40 = ordered_pair(U_38,U_37) ) )
& ( ! [U_36,U_35] :
( U_39 = U_35
| U_40 != ordered_pair(U_36,U_35) )
| U_39 != pair_second(U_40) ) )
| ! [U_34,U_33] : U_40 != ordered_pair(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_40] :
( ( ! [U_42] :
( U_42 = pair_second(U_40)
| ? [U_38,U_37] :
( U_42 != U_37
& U_40 = ordered_pair(U_38,U_37) ) )
& ! [U_41] :
( ! [U_36,U_35] :
( U_41 = U_35
| U_40 != ordered_pair(U_36,U_35) )
| U_41 != pair_second(U_40) ) )
| ! [U_34,U_33] : U_40 != ordered_pair(U_34,U_33) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_40] :
( ( ! [U_42] :
( U_42 = pair_second(U_40)
| ? [U_37] :
( U_42 != U_37
& U_40 = ordered_pair(sK10(U_40,U_42),U_37) ) )
& ! [U_41] :
( ! [U_36,U_35] :
( U_41 = U_35
| U_40 != ordered_pair(U_36,U_35) )
| U_41 != pair_second(U_40) ) )
| ! [U_34,U_33] : U_40 != ordered_pair(U_34,U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_38,sK10(U_40,U_42))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_40] :
( ( ! [U_42] :
( U_42 = pair_second(U_40)
| ( U_42 != sK11(U_40,U_42)
& U_40 = ordered_pair(sK10(U_40,U_42),sK11(U_40,U_42)) ) )
& ! [U_41] :
( ! [U_36,U_35] :
( U_41 = U_35
| U_40 != ordered_pair(U_36,U_35) )
| U_41 != pair_second(U_40) ) )
| ! [U_34,U_33] : U_40 != ordered_pair(U_34,U_33) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_37,sK11(U_40,U_42))],[f_19_4]) ).
cnf(f_19_6,plain,
( U_41 = U_35
| U_40 != ordered_pair(U_36,U_35)
| U_41 != pair_second(U_40)
| U_40 != ordered_pair(U_34,U_33) ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(t1,plain,
( pair_second(ordered_pair(sK6,sK7)) != sK7
| pair_first(ordered_pair(sK4,sK5)) != sK4 ),
inference(start,[status(thm),parent(0:0)],[f_17_10]) ).
cnf(t2,plain,
( pair_first(ordered_pair(sK4,sK5)) != pair_first(ordered_pair(sK4,sK5))
| ordered_pair(sK4,sK5) != ordered_pair(sK4,sK5)
| ordered_pair(sK4,sK5) != ordered_pair(sK4,sK5)
| pair_first(ordered_pair(sK4,sK5)) = sK4 ),
inference(extension,[status(thm),parent(t1:1)],[f_18_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
ordered_pair(sK4,sK5) = ordered_pair(sK4,sK5),
inference(extension,[status(thm),parent(t2:2)],[equality_1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
ordered_pair(sK4,sK5) = ordered_pair(sK4,sK5),
inference(extension,[status(thm),parent(t2:3)],[equality_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
pair_first(ordered_pair(sK4,sK5)) = pair_first(ordered_pair(sK4,sK5)),
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,
( pair_second(ordered_pair(sK6,sK7)) != pair_second(ordered_pair(sK6,sK7))
| ordered_pair(sK6,sK7) != ordered_pair(sK6,sK7)
| ordered_pair(sK6,sK7) != ordered_pair(sK6,sK7)
| pair_second(ordered_pair(sK6,sK7)) = sK7 ),
inference(extension,[status(thm),parent(t1:2)],[f_19_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t1:2]) ).
cnf(t12,plain,
ordered_pair(sK6,sK7) = ordered_pair(sK6,sK7),
inference(extension,[status(thm),parent(t10:2)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
ordered_pair(sK6,sK7) = ordered_pair(sK6,sK7),
inference(extension,[status(thm),parent(t10:3)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
pair_second(ordered_pair(sK6,sK7)) = pair_second(ordered_pair(sK6,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 : SEU267+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.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 23:44:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.42 % SZS status Theorem for theBenchmark
% 0.10/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------