%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /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 : Sun Sep 27 08:36:55 AM UTC 2026
% Result : Theorem 10.60s 1.88s
% Output : CNFRefutation 10.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 44 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 38 ( 10 ~; 6 |; 13 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(equivalence,axiom,
! [A,R] :
( equivalence(R,A)
<=> ( ! [X,Y,Z] :
( ( member(Z,A)
& member(Y,A)
& member(X,A) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,A)
& member(X,A) )
=> ( apply(R,X,Y)
=> apply(R,Y,X) ) )
& ! [X] :
( member(X,A)
=> apply(R,X,X) ) ) ),
file('theBenchmark.p',equivalence) ).
fof(equivalence_class,axiom,
! [R,E,A,X] :
( member(X,equivalence_class(A,E,R))
<=> ( apply(R,A,X)
& member(X,E) ) ),
file('theBenchmark.p',equivalence_class) ).
fof(thIII02,conjecture,
! [E,R,A] :
( ( member(A,E)
& equivalence(R,E) )
=> member(A,equivalence_class(A,E,R)) ),
file('theBenchmark.p',thIII02) ).
fof(thIII02_neg,negated_conjecture,
~ ! [E,R,A] :
( ( member(A,E)
& equivalence(R,E) )
=> member(A,equivalence_class(A,E,R)) ),
inference(assume_negation,[status(cth)],[thIII02]) ).
fof(nnf_17,plain,
? [E,R,A] :
( ~ member(A,equivalence_class(A,E,R))
& member(A,E)
& equivalence(R,E) ),
inference(fof_nnf,[status(thm)],[thIII02_neg]) ).
fof(sk_thIII02_neg,plain,
( ~ member(sK2,equivalence_class(sK2,sK1,sK0))
& member(sK2,sK1)
& equivalence(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(E,sK1),skolemize(R,sK0),skolemize(A,sK2)],[nnf_17]) ).
cnf(c_97,negated_conjecture,
equivalence(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_thIII02_neg]) ).
cnf(c_99,plain,
( apply(A,C,C)
| ~ member(C,B)
| ~ equivalence(A,B) ),
inference(clausify,[status(thm)],[equivalence]) ).
cnf(c_218,negated_conjecture,
~ member(sK2,equivalence_class(sK2,sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_thIII02_neg]) ).
cnf(c_219,negated_conjecture,
member(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_thIII02_neg]) ).
cnf(c_220,plain,
( ~ apply(D,B,A)
| ~ member(A,C)
| member(A,equivalence_class(B,C,D)) ),
inference(clausify,[status(thm)],[equivalence_class]) ).
cnf(c_397,negated_conjecture,
( apply(sK0,A,A)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_99,c_97]) ).
cnf(c_1568,plain,
apply(sK0,sK2,sK2),
inference(resolve,[status(thm)],[c_397,c_219]) ).
cnf(c_1608,negated_conjecture,
( ~ apply(B,A,sK2)
| member(sK2,equivalence_class(A,sK1,B)) ),
inference(resolve,[status(thm)],[c_220,c_219]) ).
cnf(c_1609,negated_conjecture,
member(sK2,equivalence_class(sK2,sK1,sK0)),
inference(resolve,[status(thm)],[c_1608,c_1568]) ).
cnf(c_1607,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_218,c_1609]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:13:51 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1204197 was started by sandbox on n004,
% 0.18/0.45 % Sat Sep 26 08:13:51 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.48
% 0.18/0.48 % From the command line: assign(max_seconds, 300).
% 10.60/1.88
% 10.60/1.88 % given #500 (I,wt=53): 613 -member(f14(A,B),A) | -member(f16(A,B),A) | -member(C,A) | -apply(B,f14(A,B),f16(A,B)) | -apply(B,f16(A,B),C) | apply(B,f14(A,B),C) | member(f11(A,B),A) | member(f12(A,B),A). [factor(256,d,i)].
% 10.60/1.88
% 10.60/1.88 % SZS status Theorem for theBenchmark
% 10.60/1.88
% 10.60/1.88 % Proof 1 at 1.26 (+ 0.12) seconds.
% 10.60/1.88 % Length of proof is 11.
% 10.60/1.88 % Level of proof is 4.
% 10.60/1.88 % Maximum clause weight is 23.000.
% 10.60/1.88 % Given clauses 713.
% 10.60/1.88
% 10.60/1.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------