%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN074+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n002.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 09:09:25 AM UTC 2026
% Result : Theorem 8.26s 8.58s
% Output : Proof 8.66s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(pel51_1,axiom,
? [Z,W] :
! [X,Y] :
( big_f(X,Y)
<=> ( Y = W
& X = Z ) ),
file('theBenchmark.p',pel51_1) ).
fof(pel51,conjecture,
? [Z] :
! [X] :
( ? [W] :
! [Y] :
( big_f(X,Y)
<=> Y = W )
<=> X = Z ),
file('theBenchmark.p',pel51) ).
fof(f_1_1,plain,
? [Z,W] :
! [X,Y] :
( ( big_f(X,Y)
| Y != W
| X != Z )
& ( ( Y = W
& X = Z )
| ~ big_f(X,Y) ) ),
inference(fof_nnf,[status(thm)],[pel51_1]) ).
fof(f_1_2,plain,
? [U_3,U_2] :
! [U_1,U_0] :
( ( big_f(U_1,U_0)
| U_0 != U_2
| U_1 != U_3 )
& ( ( U_0 = U_2
& U_1 = U_3 )
| ~ big_f(U_1,U_0) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
? [U_3,U_2] :
( ! [U_7,U_5] :
( big_f(U_7,U_5)
| U_5 != U_2
| U_7 != U_3 )
& ! [U_6,U_4] :
( ( U_4 = U_2
& U_6 = U_3 )
| ~ big_f(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
? [U_2] :
( ! [U_7,U_5] :
( big_f(U_7,U_5)
| U_5 != U_2
| U_7 != sK1 )
& ! [U_6,U_4] :
( ( U_4 = U_2
& U_6 = sK1 )
| ~ big_f(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_3]) ).
fof(f_1_5,plain,
( ! [U_7,U_5] :
( big_f(U_7,U_5)
| U_5 != sK2
| U_7 != sK1 )
& ! [U_6,U_4] :
( ( U_4 = sK2
& U_6 = sK1 )
| ~ big_f(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_1_4]) ).
cnf(f_1_6,plain,
( U_6 = sK1
| ~ big_f(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_7,plain,
( U_4 = sK2
| ~ big_f(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_5]) ).
cnf(f_1_8,plain,
( big_f(U_7,U_5)
| U_5 != sK2
| U_7 != sK1 ),
inference(clausify,[status(thm)],[f_1_5]) ).
fof(f_2_1,negated_conjecture,
~ ? [Z] :
! [X] :
( ? [W] :
! [Y] :
( big_f(X,Y)
<=> Y = W )
<=> X = Z ),
inference(negate,[status(cth)],[pel51]) ).
fof(f_2_2,negated_conjecture,
! [Z] :
? [X] :
( ( ! [W] :
? [Y] :
( ( ~ big_f(X,Y)
& Y = W )
| ( Y != W
& big_f(X,Y) ) )
& X = Z )
| ( X != Z
& ? [W] :
! [Y] :
( ( big_f(X,Y)
| Y != W )
& ( Y = W
| ~ big_f(X,Y) ) ) ) ),
inference(fof_nnf,[status(thm)],[f_2_1]) ).
fof(f_2_3,negated_conjecture,
! [U_13] :
? [U_12] :
( ( ! [U_11] :
? [U_10] :
( ( ~ big_f(U_12,U_10)
& U_10 = U_11 )
| ( U_10 != U_11
& big_f(U_12,U_10) ) )
& U_12 = U_13 )
| ( U_12 != U_13
& ? [U_9] :
! [U_8] :
( ( big_f(U_12,U_8)
| U_8 != U_9 )
& ( U_8 = U_9
| ~ big_f(U_12,U_8) ) ) ) ),
inference(variable_rename,[status(thm)],[f_2_2]) ).
fof(f_2_4,negated_conjecture,
! [U_13] :
( ? [U_19] :
( ! [U_11] :
( ? [U_17] :
( ~ big_f(U_19,U_17)
& U_17 = U_11 )
| ? [U_16] :
( U_16 != U_11
& big_f(U_19,U_16) ) )
& U_19 = U_13 )
| ? [U_18] :
( U_18 != U_13
& ? [U_9] :
( ! [U_15] :
( big_f(U_18,U_15)
| U_15 != U_9 )
& ! [U_14] :
( U_14 = U_9
| ~ big_f(U_18,U_14) ) ) ) ),
inference(miniscope,[status(thm)],[f_2_3]) ).
fof(f_2_5,negated_conjecture,
! [U_13] :
( ? [U_19] :
( ! [U_11] :
( ? [U_17] :
( ~ big_f(U_19,U_17)
& U_17 = U_11 )
| ? [U_16] :
( U_16 != U_11
& big_f(U_19,U_16) ) )
& U_19 = U_13 )
| ( sK3(U_13) != U_13
& ? [U_9] :
( ! [U_15] :
( big_f(sK3(U_13),U_15)
| U_15 != U_9 )
& ! [U_14] :
( U_14 = U_9
| ~ big_f(sK3(U_13),U_14) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3(U_13))],[f_2_4]) ).
fof(f_2_6,negated_conjecture,
! [U_13] :
( ? [U_19] :
( ! [U_11] :
( ? [U_17] :
( ~ big_f(U_19,U_17)
& U_17 = U_11 )
| ? [U_16] :
( U_16 != U_11
& big_f(U_19,U_16) ) )
& U_19 = U_13 )
| ( sK3(U_13) != U_13
& ! [U_15] :
( big_f(sK3(U_13),U_15)
| U_15 != sK4(U_13) )
& ! [U_14] :
( U_14 = sK4(U_13)
| ~ big_f(sK3(U_13),U_14) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_9,sK4(U_13))],[f_2_5]) ).
fof(f_2_7,negated_conjecture,
! [U_13] :
( ( ! [U_11] :
( ? [U_17] :
( ~ big_f(sK5(U_13),U_17)
& U_17 = U_11 )
| ? [U_16] :
( U_16 != U_11
& big_f(sK5(U_13),U_16) ) )
& sK5(U_13) = U_13 )
| ( sK3(U_13) != U_13
& ! [U_15] :
( big_f(sK3(U_13),U_15)
| U_15 != sK4(U_13) )
& ! [U_14] :
( U_14 = sK4(U_13)
| ~ big_f(sK3(U_13),U_14) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_19,sK5(U_13))],[f_2_6]) ).
fof(f_2_8,negated_conjecture,
! [U_13] :
( ( ! [U_11] :
( ? [U_17] :
( ~ big_f(sK5(U_13),U_17)
& U_17 = U_11 )
| ( sK6(U_13,U_11) != U_11
& big_f(sK5(U_13),sK6(U_13,U_11)) ) )
& sK5(U_13) = U_13 )
| ( sK3(U_13) != U_13
& ! [U_15] :
( big_f(sK3(U_13),U_15)
| U_15 != sK4(U_13) )
& ! [U_14] :
( U_14 = sK4(U_13)
| ~ big_f(sK3(U_13),U_14) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_16,sK6(U_13,U_11))],[f_2_7]) ).
fof(f_2_9,negated_conjecture,
! [U_13] :
( ( ! [U_11] :
( ( ~ big_f(sK5(U_13),sK7(U_13,U_11))
& sK7(U_13,U_11) = U_11 )
| ( sK6(U_13,U_11) != U_11
& big_f(sK5(U_13),sK6(U_13,U_11)) ) )
& sK5(U_13) = U_13 )
| ( sK3(U_13) != U_13
& ! [U_15] :
( big_f(sK3(U_13),U_15)
| U_15 != sK4(U_13) )
& ! [U_14] :
( U_14 = sK4(U_13)
| ~ big_f(sK3(U_13),U_14) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_17,sK7(U_13,U_11))],[f_2_8]) ).
fof(f_2_10,negated_conjecture,
( ! [U_11,U_13] :
( ~ big_f(sK5(U_13),sK7(U_13,U_11))
| ~ sP2(U_11,U_13) )
& ! [U_11,U_13] :
( sK7(U_13,U_11) = U_11
| ~ sP2(U_11,U_13) )
& ! [U_11,U_13] :
( sK6(U_13,U_11) != U_11
| ~ sP1(U_11,U_13) )
& ! [U_11,U_13] :
( big_f(sK5(U_13),sK6(U_13,U_11))
| ~ sP1(U_11,U_13) )
& ! [U_11,U_13] :
( sP2(U_11,U_13)
| sP1(U_11,U_13)
| ~ sP3(U_11,U_13) )
& ! [U_11,U_13] :
( sK5(U_13) = U_13
| ~ sP3(U_11,U_13) )
& ! [U_14,U_15,U_13] :
( sK3(U_13) != U_13
| ~ sP0(U_14,U_15,U_13) )
& ! [U_14,U_15,U_13] :
( big_f(sK3(U_13),U_15)
| U_15 != sK4(U_13)
| ~ sP0(U_14,U_15,U_13) )
& ! [U_14,U_15,U_13] :
( U_14 = sK4(U_13)
| ~ big_f(sK3(U_13),U_14)
| ~ sP0(U_14,U_15,U_13) )
& ! [U_11,U_14,U_15,U_13] :
( sP3(U_11,U_13)
| sP0(U_14,U_15,U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_2_9]) ).
cnf(f_2_11,negated_conjecture,
( sP3(U_11,U_13)
| sP0(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_12,negated_conjecture,
( U_14 = sK4(U_13)
| ~ big_f(sK3(U_13),U_14)
| ~ sP0(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_13,negated_conjecture,
( big_f(sK3(U_13),U_15)
| U_15 != sK4(U_13)
| ~ sP0(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_14,negated_conjecture,
( sK3(U_13) != U_13
| ~ sP0(U_14,U_15,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_15,negated_conjecture,
( sK5(U_13) = U_13
| ~ sP3(U_11,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_16,negated_conjecture,
( sP2(U_11,U_13)
| sP1(U_11,U_13)
| ~ sP3(U_11,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_17,negated_conjecture,
( big_f(sK5(U_13),sK6(U_13,U_11))
| ~ sP1(U_11,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_18,negated_conjecture,
( sK6(U_13,U_11) != U_11
| ~ sP1(U_11,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_19,negated_conjecture,
( sK7(U_13,U_11) = U_11
| ~ sP2(U_11,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(f_2_20,negated_conjecture,
( ~ big_f(sK5(U_13),sK7(U_13,U_11))
| ~ sP2(U_11,U_13) ),
inference(clausify,[status(thm)],[f_2_10]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( big_f(Eq_y_0,Eq_y_1)
| ~ big_f(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( sP0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN074+1 : TPTP v9.3.1. Released v2.0.0.
% 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
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 06:27:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 8.26/8.58 % SZS status Theorem for theBenchmark
% 8.26/8.58 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------