%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN084+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 : n004.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 09:09:27 AM UTC 2026
% Result : Theorem 0.09s 0.42s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(pel62,conjecture,
( ! [X] :
( ( ( big_p(X)
=> big_p(f(X)) )
& big_p(a) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
file('theBenchmark.p',pel62) ).
fof(f_1_1,negated_conjecture,
~ ( ! [X] :
( ( ( big_p(X)
=> big_p(f(X)) )
& big_p(a) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negate,[status(cth)],[pel62]) ).
fof(f_1_2,negated_conjecture,
( ( ? [X] :
( ~ big_p(f(f(X)))
& ( big_p(f(X))
| ~ big_p(X) )
& big_p(a) )
& ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) )
| ( ? [X1] :
( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) )
& ! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) )
| ~ big_p(a) ) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ? [U_3] :
( ~ big_p(f(f(U_3)))
& ( big_p(f(U_3))
| ~ big_p(U_3) )
& big_p(a) )
& ! [U_2] :
( ( big_p(f(f(U_2)))
| ~ big_p(f(U_2))
| ~ big_p(a) )
& ( big_p(f(f(U_2)))
| big_p(U_2)
| ~ big_p(a) ) ) )
| ( ? [U_1] :
( ( ~ big_p(f(f(U_1)))
& big_p(f(U_1))
& big_p(a) )
| ( ~ big_p(f(f(U_1)))
& ~ big_p(U_1)
& big_p(a) ) )
& ! [U_0] :
( big_p(f(f(U_0)))
| ( ~ big_p(f(U_0))
& big_p(U_0) )
| ~ big_p(a) ) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ? [U_3] :
( ~ big_p(f(f(U_3)))
& ( big_p(f(U_3))
| ~ big_p(U_3) )
& big_p(a) )
& ( ! [U_7] :
( big_p(f(f(U_7)))
| ~ big_p(f(U_7)) )
| ~ big_p(a) )
& ( ! [U_6] :
( big_p(f(f(U_6)))
| big_p(U_6) )
| ~ big_p(a) ) )
| ( ( ( ? [U_5] :
( ~ big_p(f(f(U_5)))
& big_p(f(U_5)) )
& big_p(a) )
| ( ? [U_4] :
( ~ big_p(f(f(U_4)))
& ~ big_p(U_4) )
& big_p(a) ) )
& ! [U_0] :
( big_p(f(f(U_0)))
| ( ~ big_p(f(U_0))
& big_p(U_0) )
| ~ big_p(a) ) ) ),
inference(miniscope,[status(thm)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ? [U_3] :
( ~ big_p(f(f(U_3)))
& ( big_p(f(U_3))
| ~ big_p(U_3) )
& big_p(a) )
& ( ! [U_7] :
( big_p(f(f(U_7)))
| ~ big_p(f(U_7)) )
| ~ big_p(a) )
& ( ! [U_6] :
( big_p(f(f(U_6)))
| big_p(U_6) )
| ~ big_p(a) ) )
| ( ( ( ? [U_5] :
( ~ big_p(f(f(U_5)))
& big_p(f(U_5)) )
& big_p(a) )
| ( ~ big_p(f(f(sK1)))
& ~ big_p(sK1)
& big_p(a) ) )
& ! [U_0] :
( big_p(f(f(U_0)))
| ( ~ big_p(f(U_0))
& big_p(U_0) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_4,sK1)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ? [U_3] :
( ~ big_p(f(f(U_3)))
& ( big_p(f(U_3))
| ~ big_p(U_3) )
& big_p(a) )
& ( ! [U_7] :
( big_p(f(f(U_7)))
| ~ big_p(f(U_7)) )
| ~ big_p(a) )
& ( ! [U_6] :
( big_p(f(f(U_6)))
| big_p(U_6) )
| ~ big_p(a) ) )
| ( ( ( ~ big_p(f(f(sK2)))
& big_p(f(sK2))
& big_p(a) )
| ( ~ big_p(f(f(sK1)))
& ~ big_p(sK1)
& big_p(a) ) )
& ! [U_0] :
( big_p(f(f(U_0)))
| ( ~ big_p(f(U_0))
& big_p(U_0) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ~ big_p(f(f(sK3)))
& ( big_p(f(sK3))
| ~ big_p(sK3) )
& big_p(a)
& ( ! [U_7] :
( big_p(f(f(U_7)))
| ~ big_p(f(U_7)) )
| ~ big_p(a) )
& ( ! [U_6] :
( big_p(f(f(U_6)))
| big_p(U_6) )
| ~ big_p(a) ) )
| ( ( ( ~ big_p(f(f(sK2)))
& big_p(f(sK2))
& big_p(a) )
| ( ~ big_p(f(f(sK1)))
& ~ big_p(sK1)
& big_p(a) ) )
& ! [U_0] :
( big_p(f(f(U_0)))
| ( ~ big_p(f(U_0))
& big_p(U_0) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_3,sK3)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ! [U_7,U_6] :
( ~ big_p(f(f(sK3)))
| ~ sP4(U_7,U_6) )
& ! [U_7,U_6] :
( big_p(f(sK3))
| ~ big_p(sK3)
| ~ sP4(U_7,U_6) )
& ! [U_7,U_6] :
( big_p(a)
| ~ sP4(U_7,U_6) )
& ! [U_7,U_6] :
( big_p(f(f(U_7)))
| ~ big_p(f(U_7))
| ~ big_p(a)
| ~ sP4(U_7,U_6) )
& ! [U_7,U_6] :
( big_p(f(f(U_6)))
| big_p(U_6)
| ~ big_p(a)
| ~ sP4(U_7,U_6) )
& ( ~ big_p(f(f(sK2)))
| ~ sP2 )
& ( big_p(f(sK2))
| ~ sP2 )
& ( big_p(a)
| ~ sP2 )
& ( ~ big_p(f(f(sK1)))
| ~ sP1 )
& ( ~ big_p(sK1)
| ~ sP1 )
& ( big_p(a)
| ~ sP1 )
& ! [U_0] :
( ~ big_p(f(U_0))
| ~ sP0(U_0) )
& ! [U_0] :
( big_p(U_0)
| ~ sP0(U_0) )
& ! [U_0] :
( sP2
| sP1
| ~ sP3(U_0) )
& ! [U_0] :
( big_p(f(f(U_0)))
| sP0(U_0)
| ~ big_p(a)
| ~ sP3(U_0) )
& ! [U_0,U_7,U_6] :
( sP4(U_7,U_6)
| sP3(U_0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4])],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
( sP4(U_7,U_6)
| sP3(U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
( big_p(f(f(U_0)))
| sP0(U_0)
| ~ big_p(a)
| ~ sP3(U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
( sP2
| sP1
| ~ sP3(U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
( big_p(U_0)
| ~ sP0(U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_13,negated_conjecture,
( ~ big_p(f(U_0))
| ~ sP0(U_0) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_14,negated_conjecture,
( big_p(a)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
( ~ big_p(sK1)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
( ~ big_p(f(f(sK1)))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
( big_p(a)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_18,negated_conjecture,
( big_p(f(sK2))
| ~ sP2 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_19,negated_conjecture,
( ~ big_p(f(f(sK2)))
| ~ sP2 ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_20,negated_conjecture,
( big_p(f(f(U_6)))
| big_p(U_6)
| ~ big_p(a)
| ~ sP4(U_7,U_6) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_21,negated_conjecture,
( big_p(f(f(U_7)))
| ~ big_p(f(U_7))
| ~ big_p(a)
| ~ sP4(U_7,U_6) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_22,negated_conjecture,
( big_p(a)
| ~ sP4(U_7,U_6) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_23,negated_conjecture,
( big_p(f(sK3))
| ~ big_p(sK3)
| ~ sP4(U_7,U_6) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_24,negated_conjecture,
( ~ big_p(f(f(sK3)))
| ~ sP4(U_7,U_6) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ 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
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 06:24:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.42 % SZS status Theorem for theBenchmark
% 0.09/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------