%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n009.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 09:10:12 AM UTC 2026
% Result : Theorem 0.22s 0.55s
% Output : Proof 0.31s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(x2126,conjecture,
( ! [X] :
( big_p(X)
<=> ? [Y] : big_p(Y) )
<=> ( ! [X] : big_p(X)
<=> ? [Y] : big_p(Y) ) ),
file('theBenchmark.p',x2126) ).
fof(f_1_1,negated_conjecture,
~ ( ! [X] :
( big_p(X)
<=> ? [Y] : big_p(Y) )
<=> ( ! [X] : big_p(X)
<=> ? [Y] : big_p(Y) ) ),
inference(negate,[status(cth)],[x2126]) ).
fof(f_1_2,negated_conjecture,
( ( ? [X] :
( ( ~ big_p(X)
& ? [Y] : big_p(Y) )
| ( ! [Y] : ~ big_p(Y)
& big_p(X) ) )
& ( ! [X] : big_p(X)
| ! [Y] : ~ big_p(Y) )
& ( ? [Y] : big_p(Y)
| ? [X] : ~ big_p(X) ) )
| ( ( ( ? [X] : ~ big_p(X)
& ? [Y] : big_p(Y) )
| ( ! [Y] : ~ big_p(Y)
& ! [X] : big_p(X) ) )
& ! [X] :
( ( big_p(X)
| ! [Y] : ~ big_p(Y) )
& ( ? [Y] : big_p(Y)
| ~ big_p(X) ) ) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ? [U_13] :
( ( ~ big_p(U_13)
& ? [U_12] : big_p(U_12) )
| ( ! [U_11] : ~ big_p(U_11)
& big_p(U_13) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( ? [U_8] : big_p(U_8)
| ? [U_7] : ~ big_p(U_7) ) )
| ( ( ( ? [U_6] : ~ big_p(U_6)
& ? [U_5] : big_p(U_5) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ! [U_2] :
( ( big_p(U_2)
| ! [U_1] : ~ big_p(U_1) )
& ( ? [U_0] : big_p(U_0)
| ~ big_p(U_2) ) ) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( ? [U_16] : big_p(U_16)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( ? [U_8] : big_p(U_8)
| ? [U_7] : ~ big_p(U_7) ) )
| ( ( ( ? [U_6] : ~ big_p(U_6)
& ? [U_5] : big_p(U_5) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| ? [U_0] : big_p(U_0) ) ) ),
inference(miniscope,[status(thm)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( ? [U_16] : big_p(U_16)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( ? [U_8] : big_p(U_8)
| ? [U_7] : ~ big_p(U_7) ) )
| ( ( ( ? [U_6] : ~ big_p(U_6)
& ? [U_5] : big_p(U_5) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( ? [U_16] : big_p(U_16)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( ? [U_8] : big_p(U_8)
| ? [U_7] : ~ big_p(U_7) ) )
| ( ( ( ? [U_6] : ~ big_p(U_6)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( ? [U_16] : big_p(U_16)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( ? [U_8] : big_p(U_8)
| ? [U_7] : ~ big_p(U_7) ) )
| ( ( ( ~ big_p(sK3)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_6,sK3)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( ? [U_16] : big_p(U_16)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( ? [U_8] : big_p(U_8)
| ~ big_p(sK4) ) )
| ( ( ( ~ big_p(sK3)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_7,sK4)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( ? [U_16] : big_p(U_16)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( big_p(sK5)
| ~ big_p(sK4) ) )
| ( ( ( ~ big_p(sK3)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_8,sK5)],[f_1_8]) ).
fof(f_1_10,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& ? [U_12] : big_p(U_12) )
| ( big_p(sK6)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( big_p(sK5)
| ~ big_p(sK4) ) )
| ( ( ( ~ big_p(sK3)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_16,sK6)],[f_1_9]) ).
fof(f_1_11,negated_conjecture,
( ( ( ( ? [U_17] : ~ big_p(U_17)
& big_p(sK7) )
| ( big_p(sK6)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( big_p(sK5)
| ~ big_p(sK4) ) )
| ( ( ( ~ big_p(sK3)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_12,sK7)],[f_1_10]) ).
fof(f_1_12,negated_conjecture,
( ( ( ( ~ big_p(sK8)
& big_p(sK7) )
| ( big_p(sK6)
& ! [U_11] : ~ big_p(U_11) ) )
& ( ! [U_10] : big_p(U_10)
| ! [U_9] : ~ big_p(U_9) )
& ( big_p(sK5)
| ~ big_p(sK4) ) )
| ( ( ( ~ big_p(sK3)
& big_p(sK2) )
| ( ! [U_4] : ~ big_p(U_4)
& ! [U_3] : big_p(U_3) ) )
& ( ! [U_15] : big_p(U_15)
| ! [U_1] : ~ big_p(U_1) )
& ( ! [U_14] : ~ big_p(U_14)
| big_p(sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_17,sK8)],[f_1_11]) ).
fof(f_1_13,negated_conjecture,
( ( ~ big_p(sK8)
| ~ sP4 )
& ( big_p(sK7)
| ~ sP4 )
& ! [U_11] :
( big_p(sK6)
| ~ sP3(U_11) )
& ! [U_11] :
( ~ big_p(U_11)
| ~ sP3(U_11) )
& ! [U_9,U_11,U_10] :
( sP4
| sP3(U_11)
| ~ sP5(U_9,U_11,U_10) )
& ! [U_9,U_11,U_10] :
( big_p(U_10)
| ~ big_p(U_9)
| ~ sP5(U_9,U_11,U_10) )
& ! [U_9,U_11,U_10] :
( big_p(sK5)
| ~ big_p(sK4)
| ~ sP5(U_9,U_11,U_10) )
& ( ~ big_p(sK3)
| ~ sP1 )
& ( big_p(sK2)
| ~ sP1 )
& ! [U_4,U_3] :
( ~ big_p(U_4)
| ~ sP0(U_4,U_3) )
& ! [U_4,U_3] :
( big_p(U_3)
| ~ sP0(U_4,U_3) )
& ! [U_4,U_1,U_3,U_15,U_14] :
( sP1
| sP0(U_4,U_3)
| ~ sP2(U_4,U_1,U_3,U_15,U_14) )
& ! [U_4,U_1,U_3,U_15,U_14] :
( big_p(U_15)
| ~ big_p(U_1)
| ~ sP2(U_4,U_1,U_3,U_15,U_14) )
& ! [U_4,U_1,U_3,U_15,U_14] :
( ~ big_p(U_14)
| big_p(sK1)
| ~ sP2(U_4,U_1,U_3,U_15,U_14) )
& ! [U_9,U_4,U_11,U_10,U_1,U_3,U_15,U_14] :
( sP5(U_9,U_11,U_10)
| sP2(U_4,U_1,U_3,U_15,U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4,sP5])],[f_1_12]) ).
cnf(f_1_14,negated_conjecture,
( sP5(U_9,U_11,U_10)
| sP2(U_4,U_1,U_3,U_15,U_14) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_15,negated_conjecture,
( ~ big_p(U_14)
| big_p(sK1)
| ~ sP2(U_4,U_1,U_3,U_15,U_14) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_16,negated_conjecture,
( big_p(U_15)
| ~ big_p(U_1)
| ~ sP2(U_4,U_1,U_3,U_15,U_14) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_17,negated_conjecture,
( sP1
| sP0(U_4,U_3)
| ~ sP2(U_4,U_1,U_3,U_15,U_14) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_18,negated_conjecture,
( big_p(U_3)
| ~ sP0(U_4,U_3) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_19,negated_conjecture,
( ~ big_p(U_4)
| ~ sP0(U_4,U_3) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_20,negated_conjecture,
( big_p(sK2)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_21,negated_conjecture,
( ~ big_p(sK3)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_22,negated_conjecture,
( big_p(sK5)
| ~ big_p(sK4)
| ~ sP5(U_9,U_11,U_10) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_23,negated_conjecture,
( big_p(U_10)
| ~ big_p(U_9)
| ~ sP5(U_9,U_11,U_10) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_24,negated_conjecture,
( sP4
| sP3(U_11)
| ~ sP5(U_9,U_11,U_10) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_25,negated_conjecture,
( ~ big_p(U_11)
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_26,negated_conjecture,
( big_p(sK6)
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_27,negated_conjecture,
( big_p(sK7)
| ~ sP4 ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(f_1_28,negated_conjecture,
( ~ big_p(sK8)
| ~ sP4 ),
inference(clausify,[status(thm)],[f_1_13]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 This is a FOF_THM_RFO_NEQ 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
% 0.09/0.36 % Computer : n009.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 06:29:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.22/0.55 % SZS status Theorem for theBenchmark
% 0.22/0.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------