%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO578+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 : Sun Sep 27 09:51:02 AM UTC 2026
% Result : Theorem 1.44s 0.70s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 144 ( 49 ~; 46 |; 42 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 26 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_21,axiom,
( ? [X62] :
( ~ k04_buttercup10100(X62)
& b48_buttercup10098(X62) )
& ! [X61] :
( k04_buttercup10100(X61)
=> b48_buttercup10098(X61) ) ),
file('theBenchmark.p',sos_21) ).
fof(goals_86,conjecture,
( ! [X149] :
( k04_buttercup10100(X149)
=> ~ b48_buttercup10098(X149) )
| ? [X146,X147,X148] :
( b48_buttercup10098(X148)
& ~ k04_buttercup10100(X148)
& ~ b48_buttercup10098(X147)
& k04_buttercup10100(X147)
& b48_buttercup10098(X146)
& k04_buttercup10100(X146) )
| ( ? [X145] :
( ~ k04_buttercup10100(X145)
& b48_buttercup10098(X145) )
& ! [X144] :
( k04_buttercup10100(X144)
=> b48_buttercup10098(X144) ) )
| ( ? [X143] :
( ~ b48_buttercup10098(X143)
& k04_buttercup10100(X143) )
& ! [X142] :
( b48_buttercup10098(X142)
=> k04_buttercup10100(X142) ) ) ),
file('theBenchmark.p',goals_86) ).
fof(goals_86_neg,negated_conjecture,
~ ( ! [X149] :
( k04_buttercup10100(X149)
=> ~ b48_buttercup10098(X149) )
| ? [X146,X147,X148] :
( b48_buttercup10098(X148)
& ~ k04_buttercup10100(X148)
& ~ b48_buttercup10098(X147)
& k04_buttercup10100(X147)
& b48_buttercup10098(X146)
& k04_buttercup10100(X146) )
| ( ? [X145] :
( ~ k04_buttercup10100(X145)
& b48_buttercup10098(X145) )
& ! [X144] :
( k04_buttercup10100(X144)
=> b48_buttercup10098(X144) ) )
| ( ? [X143] :
( ~ b48_buttercup10098(X143)
& k04_buttercup10100(X143) )
& ! [X142] :
( b48_buttercup10098(X142)
=> k04_buttercup10100(X142) ) ) ),
inference(assume_negation,[status(cth)],[goals_86]) ).
fof(nnf_21,plain,
( ? [X62] :
( ~ k04_buttercup10100(X62)
& b48_buttercup10098(X62) )
& ! [X61] :
( b48_buttercup10098(X61)
| ~ k04_buttercup10100(X61) ) ),
inference(fof_nnf,[status(thm)],[sos_21]) ).
fof(sk_sos_21,plain,
( ~ k04_buttercup10100(sK0)
& b48_buttercup10098(sK0)
& ! [X61] :
( b48_buttercup10098(X61)
| ~ k04_buttercup10100(X61) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X62,sK0)],[nnf_21]) ).
cnf(c_418,plain,
( b48_buttercup10098(A)
| ~ k04_buttercup10100(A) ),
inference(split_conjunct,[status(thm)],[sk_sos_21]) ).
cnf(c_419,plain,
b48_buttercup10098(sK0),
inference(split_conjunct,[status(thm)],[sk_sos_21]) ).
cnf(c_420,plain,
~ k04_buttercup10100(sK0),
inference(split_conjunct,[status(thm)],[sk_sos_21]) ).
fof(nnf_86,plain,
( ? [X149] :
( b48_buttercup10098(X149)
& k04_buttercup10100(X149) )
& ! [X146,X147,X148] :
( ~ b48_buttercup10098(X148)
| k04_buttercup10100(X148)
| b48_buttercup10098(X147)
| ~ k04_buttercup10100(X147)
| ~ b48_buttercup10098(X146)
| ~ k04_buttercup10100(X146) )
& ( ! [X145] :
( k04_buttercup10100(X145)
| ~ b48_buttercup10098(X145) )
| ? [X144] :
( ~ b48_buttercup10098(X144)
& k04_buttercup10100(X144) ) )
& ( ! [X143] :
( b48_buttercup10098(X143)
| ~ k04_buttercup10100(X143) )
| ? [X142] :
( ~ k04_buttercup10100(X142)
& b48_buttercup10098(X142) ) ) ),
inference(fof_nnf,[status(thm)],[goals_86_neg]) ).
fof(sk_goals_86_neg_sk,plain,
( b48_buttercup10098(sK3)
& k04_buttercup10100(sK3)
& ! [X146,X147,X148] :
( ~ b48_buttercup10098(X148)
| k04_buttercup10100(X148)
| b48_buttercup10098(X147)
| ~ k04_buttercup10100(X147)
| ~ b48_buttercup10098(X146)
| ~ k04_buttercup10100(X146) )
& ( ! [X145] :
( k04_buttercup10100(X145)
| ~ b48_buttercup10098(X145) )
| ( ~ b48_buttercup10098(sK1)
& k04_buttercup10100(sK1) ) )
& ( ! [X143] :
( b48_buttercup10098(X143)
| ~ k04_buttercup10100(X143) )
| ( ~ k04_buttercup10100(sK2)
& b48_buttercup10098(sK2) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK3]),skolemize(X142,sK2),skolemize(X144,sK1),skolemize(X149,sK3)],[nnf_86]) ).
fof(sk_goals_86_neg,plain,
( b48_buttercup10098(sK3)
& k04_buttercup10100(sK3)
& ! [VAR_0,VAR_1,VAR_2] :
( ~ b48_buttercup10098(VAR_2)
| k04_buttercup10100(VAR_2)
| b48_buttercup10098(VAR_1)
| ~ k04_buttercup10100(VAR_1)
| ~ b48_buttercup10098(VAR_0)
| ~ k04_buttercup10100(VAR_0) )
& ! [VAR_0] :
( k04_buttercup10100(VAR_0)
| ~ b48_buttercup10098(VAR_0)
| ~ b48_buttercup10098(sK1) )
& ! [VAR_0] :
( k04_buttercup10100(VAR_0)
| ~ b48_buttercup10098(VAR_0)
| k04_buttercup10100(sK1) )
& ! [VAR_0] :
( b48_buttercup10098(VAR_0)
| ~ k04_buttercup10100(VAR_0)
| ~ k04_buttercup10100(sK2) )
& ! [VAR_0] :
( b48_buttercup10098(VAR_0)
| ~ k04_buttercup10100(VAR_0)
| b48_buttercup10098(sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_86_neg_sk]) ).
cnf(c_559,negated_conjecture,
( k04_buttercup10100(A)
| ~ b48_buttercup10098(A)
| k04_buttercup10100(sK1) ),
inference(split_conjunct,[status(thm)],[sk_goals_86_neg]) ).
cnf(c_560,negated_conjecture,
( k04_buttercup10100(A)
| ~ b48_buttercup10098(A)
| ~ b48_buttercup10098(sK1) ),
inference(split_conjunct,[status(thm)],[sk_goals_86_neg]) ).
cnf(c_2075,negated_conjecture,
( k04_buttercup10100(sK0)
| k04_buttercup10100(sK1) ),
inference(resolve,[status(thm)],[c_559,c_419]) ).
cnf(c_1796,negated_conjecture,
k04_buttercup10100(sK1),
inference(resolve,[status(thm)],[c_420,c_2075]) ).
cnf(c_2076,negated_conjecture,
( k04_buttercup10100(sK0)
| ~ b48_buttercup10098(sK1) ),
inference(resolve,[status(thm)],[c_560,c_419]) ).
cnf(c_1798,negated_conjecture,
~ b48_buttercup10098(sK1),
inference(resolve,[status(thm)],[c_420,c_2076]) ).
cnf(c_2077,plain,
b48_buttercup10098(sK1),
inference(resolve,[status(thm)],[c_1796,c_418]) ).
cnf(c_2074,plain,
$false,
inference(resolve,[status(thm)],[c_1798,c_2077]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO578+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n002.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 19:32:51 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 2515443 was started by sandbox2 on n002,
% 0.08/0.38 % Sat Sep 26 19:32:51 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.44
% 0.08/0.44 % From the command line: assign(max_seconds, 300).
% 1.44/0.70
% 1.44/0.70 % given #500 (I,wt=13): 606 -b48_buttercup10104(c2) | -b48_buttercup10104(c4) | -k04_buttercup10100(c5) | -k04_buttercup10100(c4). [factor(171,b,e)].
% 1.44/0.70
% 1.44/0.70 % SZS status Theorem for theBenchmark
% 1.44/0.70
% 1.44/0.70 % Proof 1 at 0.22 (+ 0.03) seconds.
% 1.44/0.70 % Length of proof is 10.
% 1.44/0.70 % Level of proof is 3.
% 1.44/0.70 % Maximum clause weight is 11.000.
% 1.44/0.70 % Given clauses 920.
% 1.44/0.70
% 1.44/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------