%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN078+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 : n013.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 09:09:26 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Proof 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(pel56,conjecture,
( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
file('theBenchmark.p',pel56) ).
fof(f_1_1,negated_conjecture,
~ ( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
inference(negate,[status(cth)],[pel56]) ).
fof(f_1_2,negated_conjecture,
( ( ? [X] :
( ~ big_p(X)
& ? [Y] :
( X = f(Y)
& big_p(Y) ) )
& ! [U] :
( big_p(f(U))
| ~ big_p(U) ) )
| ( ? [U] :
( ~ big_p(f(U))
& big_p(U) )
& ! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) ) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ? [U_5] :
( ~ big_p(U_5)
& ? [U_4] :
( U_5 = f(U_4)
& big_p(U_4) ) )
& ! [U_3] :
( big_p(f(U_3))
| ~ big_p(U_3) ) )
| ( ? [U_2] :
( ~ big_p(f(U_2))
& big_p(U_2) )
& ! [U_1] :
( big_p(U_1)
| ! [U_0] :
( U_1 != f(U_0)
| ~ big_p(U_0) ) ) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ? [U_5] :
( ~ big_p(U_5)
& ? [U_4] :
( U_5 = f(U_4)
& big_p(U_4) ) )
& ! [U_3] :
( big_p(f(U_3))
| ~ big_p(U_3) ) )
| ( ~ big_p(f(sK1))
& big_p(sK1)
& ! [U_1] :
( big_p(U_1)
| ! [U_0] :
( U_1 != f(U_0)
| ~ big_p(U_0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ~ big_p(sK2)
& ? [U_4] :
( sK2 = f(U_4)
& big_p(U_4) )
& ! [U_3] :
( big_p(f(U_3))
| ~ big_p(U_3) ) )
| ( ~ big_p(f(sK1))
& big_p(sK1)
& ! [U_1] :
( big_p(U_1)
| ! [U_0] :
( U_1 != f(U_0)
| ~ big_p(U_0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ~ big_p(sK2)
& sK2 = f(sK3)
& big_p(sK3)
& ! [U_3] :
( big_p(f(U_3))
| ~ big_p(U_3) ) )
| ( ~ big_p(f(sK1))
& big_p(sK1)
& ! [U_1] :
( big_p(U_1)
| ! [U_0] :
( U_1 != f(U_0)
| ~ big_p(U_0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_4,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ! [U_3] :
( ~ big_p(sK2)
| ~ sP1(U_3) )
& ! [U_3] :
( sK2 = f(sK3)
| ~ sP1(U_3) )
& ! [U_3] :
( big_p(sK3)
| ~ sP1(U_3) )
& ! [U_3] :
( big_p(f(U_3))
| ~ big_p(U_3)
| ~ sP1(U_3) )
& ! [U_1,U_0] :
( ~ big_p(f(sK1))
| ~ sP0(U_1,U_0) )
& ! [U_1,U_0] :
( big_p(sK1)
| ~ sP0(U_1,U_0) )
& ! [U_1,U_0] :
( big_p(U_1)
| U_1 != f(U_0)
| ~ big_p(U_0)
| ~ sP0(U_1,U_0) )
& ! [U_3,U_1,U_0] :
( sP1(U_3)
| sP0(U_1,U_0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
( sP1(U_3)
| sP0(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
( big_p(U_1)
| U_1 != f(U_0)
| ~ big_p(U_0)
| ~ sP0(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,negated_conjecture,
( big_p(sK1)
| ~ sP0(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,negated_conjecture,
( ~ big_p(f(sK1))
| ~ sP0(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,negated_conjecture,
( big_p(f(U_3))
| ~ big_p(U_3)
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,negated_conjecture,
( big_p(sK3)
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,negated_conjecture,
( sK2 = f(sK3)
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,negated_conjecture,
( ~ big_p(sK2)
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_7]) ).
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,
( f(Eq_x_0) = f(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( big_p(Eq_y_0)
| ~ big_p(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_6,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| 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 : SYN078+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
% 0.09/0.35 % Computer : n013.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 : Sun Sep 20 06:23:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------