%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYO580+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 1.41s 0.93s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 115 ( 37 ~; 38 |; 31 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 29 ( 0 sgn 17 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_320,axiom,
( ? [X320] :
( ~ b48_buttercup10305(X320)
& k04_buttercup10303(X320) )
& ! [X319] :
( b48_buttercup10305(X319)
=> k04_buttercup10303(X319) ) ),
file('theBenchmark.p',sos_320) ).
fof(goals_886,conjecture,
( ! [X1060] :
( b48_buttercup10305(X1060)
=> ~ k04_buttercup10303(X1060) )
| ( ? [X1059] :
( ~ b48_buttercup10305(X1059)
& k04_buttercup10303(X1059) )
& ! [X1058] :
( b48_buttercup10305(X1058)
=> k04_buttercup10303(X1058) ) )
| ( ? [X1057] :
( ~ k04_buttercup10303(X1057)
& b48_buttercup10305(X1057) )
& ! [X1056] :
( k04_buttercup10303(X1056)
=> b48_buttercup10305(X1056) ) )
| ! [X1055] :
( b48_buttercup10305(X1055)
<=> k04_buttercup10303(X1055) ) ),
file('theBenchmark.p',goals_886) ).
fof(goals_886_neg,negated_conjecture,
~ ( ! [X1060] :
( b48_buttercup10305(X1060)
=> ~ k04_buttercup10303(X1060) )
| ( ? [X1059] :
( ~ b48_buttercup10305(X1059)
& k04_buttercup10303(X1059) )
& ! [X1058] :
( b48_buttercup10305(X1058)
=> k04_buttercup10303(X1058) ) )
| ( ? [X1057] :
( ~ k04_buttercup10303(X1057)
& b48_buttercup10305(X1057) )
& ! [X1056] :
( k04_buttercup10303(X1056)
=> b48_buttercup10305(X1056) ) )
| ! [X1055] :
( b48_buttercup10305(X1055)
<=> k04_buttercup10303(X1055) ) ),
inference(assume_negation,[status(cth)],[goals_886]) ).
cnf(c_2675,plain,
( k04_buttercup10303(A)
| ~ b48_buttercup10305(A) ),
inference(clausify,[status(thm)],[sos_320]) ).
fof(nnf_886,plain,
( ? [X1060] :
( k04_buttercup10303(X1060)
& b48_buttercup10305(X1060) )
& ( ! [X1059] :
( b48_buttercup10305(X1059)
| ~ k04_buttercup10303(X1059) )
| ? [X1058] :
( ~ k04_buttercup10303(X1058)
& b48_buttercup10305(X1058) ) )
& ( ! [X1057] :
( k04_buttercup10303(X1057)
| ~ b48_buttercup10305(X1057) )
| ? [X1056] :
( ~ b48_buttercup10305(X1056)
& k04_buttercup10303(X1056) ) )
& ? [X1055] :
( ( ~ k04_buttercup10303(X1055)
| ~ b48_buttercup10305(X1055) )
& ( k04_buttercup10303(X1055)
| b48_buttercup10305(X1055) ) ) ),
inference(fof_nnf,[status(thm)],[goals_886_neg]) ).
fof(sk_goals_886_neg_sk,plain,
( k04_buttercup10303(sK4)
& b48_buttercup10305(sK4)
& ( ! [X1059] :
( b48_buttercup10305(X1059)
| ~ k04_buttercup10303(X1059) )
| ( ~ k04_buttercup10303(sK1)
& b48_buttercup10305(sK1) ) )
& ( ! [X1057] :
( k04_buttercup10303(X1057)
| ~ b48_buttercup10305(X1057) )
| ( ~ b48_buttercup10305(sK3)
& k04_buttercup10303(sK3) ) )
& ( ~ k04_buttercup10303(sK0)
| ~ b48_buttercup10305(sK0) )
& ( k04_buttercup10303(sK0)
| b48_buttercup10305(sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK1,sK4]),skolemize(X1055,sK0),skolemize(X1056,sK3),skolemize(X1058,sK1),skolemize(X1060,sK4)],[nnf_886]) ).
fof(sk_goals_886_neg,plain,
( k04_buttercup10303(sK4)
& b48_buttercup10305(sK4)
& ! [VAR_0] :
( b48_buttercup10305(VAR_0)
| ~ k04_buttercup10303(VAR_0)
| ~ k04_buttercup10303(sK1) )
& ! [VAR_0] :
( b48_buttercup10305(VAR_0)
| ~ k04_buttercup10303(VAR_0)
| b48_buttercup10305(sK1) )
& ! [VAR_0] :
( k04_buttercup10303(VAR_0)
| ~ b48_buttercup10305(VAR_0)
| ~ b48_buttercup10305(sK3) )
& ! [VAR_0] :
( k04_buttercup10303(VAR_0)
| ~ b48_buttercup10305(VAR_0)
| k04_buttercup10303(sK3) )
& ( ~ k04_buttercup10303(sK0)
| ~ b48_buttercup10305(sK0) )
& ( k04_buttercup10303(sK0)
| b48_buttercup10305(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_886_neg_sk]) ).
cnf(c_2696,negated_conjecture,
( k04_buttercup10303(sK0)
| b48_buttercup10305(sK0) ),
inference(split_conjunct,[status(thm)],[sk_goals_886_neg]) ).
cnf(c_2697,negated_conjecture,
( ~ k04_buttercup10303(sK0)
| ~ b48_buttercup10305(sK0) ),
inference(split_conjunct,[status(thm)],[sk_goals_886_neg]) ).
cnf(c_2698,negated_conjecture,
( b48_buttercup10305(A)
| ~ k04_buttercup10303(A)
| b48_buttercup10305(sK1) ),
inference(split_conjunct,[status(thm)],[sk_goals_886_neg]) ).
cnf(c_2699,negated_conjecture,
( b48_buttercup10305(A)
| ~ k04_buttercup10303(A)
| ~ k04_buttercup10303(sK1) ),
inference(split_conjunct,[status(thm)],[sk_goals_886_neg]) ).
cnf(c_2742,negated_conjecture,
( k04_buttercup10303(sK0)
| k04_buttercup10303(sK0) ),
inference(resolve,[status(thm)],[c_2696,c_2675]) ).
cnf(c_2731,negated_conjecture,
k04_buttercup10303(sK0),
inference(copy,[status(thm)],[c_2742]) ).
cnf(c_2732,negated_conjecture,
~ b48_buttercup10305(sK0),
inference(resolve,[status(thm)],[c_2731,c_2697]) ).
cnf(c_2743,negated_conjecture,
( b48_buttercup10305(sK0)
| b48_buttercup10305(sK1) ),
inference(resolve,[status(thm)],[c_2698,c_2731]) ).
cnf(c_2738,negated_conjecture,
b48_buttercup10305(sK1),
inference(resolve,[status(thm)],[c_2732,c_2743]) ).
cnf(c_2744,negated_conjecture,
( b48_buttercup10305(sK0)
| ~ k04_buttercup10303(sK1) ),
inference(resolve,[status(thm)],[c_2699,c_2731]) ).
cnf(c_2739,negated_conjecture,
~ k04_buttercup10303(sK1),
inference(resolve,[status(thm)],[c_2732,c_2744]) ).
cnf(c_2745,plain,
k04_buttercup10303(sK1),
inference(resolve,[status(thm)],[c_2738,c_2675]) ).
cnf(c_2741,plain,
$false,
inference(resolve,[status(thm)],[c_2739,c_2745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO580+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.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 : Sat Sep 26 19:31:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2354867 was started by sandbox on n020,
% 0.10/0.37 % Sat Sep 26 19:31:19 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.32/0.59
% 0.32/0.59 % From the command line: assign(max_seconds, 300).
% 0.32/0.59
% 0.32/0.59 % SInE: 17 to sos, 868 to usable, of 885 axioms (tolerance 2.00, depth 0 fixpoint).
% 1.41/0.93
% 1.41/0.93 % SZS status Theorem for theBenchmark
% 1.41/0.93
% 1.41/0.93 % Proof 1 at 0.16 (+ 0.05) seconds.
% 1.41/0.93 % Length of proof is 12.
% 1.41/0.93 % Level of proof is 5.
% 1.41/0.93 % Maximum clause weight is 11.000.
% 1.41/0.93 % Given clauses 69.
% 1.41/0.93
% 1.41/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------