%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 72.69s 10.62s
% Output : CNFRefutation 72.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 77 ( 29 ~; 26 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 5 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(equal_set,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',equal_set) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('theBenchmark.p',empty_set) ).
fof(inverse_image2,axiom,
! [F,B,X] :
( member(X,inverse_image2(F,B))
<=> ? [Y] :
( apply(F,X,Y)
& member(Y,B) ) ),
file('theBenchmark.p',inverse_image2) ).
fof(thIIa14,conjecture,
! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
file('theBenchmark.p',thIIa14) ).
fof(thIIa14_neg,negated_conjecture,
~ ! [F,A,B] :
( maps(F,A,B)
=> equal_set(inverse_image2(F,empty_set),empty_set) ),
inference(assume_negation,[status(cth)],[thIIa14]) ).
fof(nnf_29,plain,
? [F,A,B] :
( ~ equal_set(inverse_image2(F,empty_set),empty_set)
& maps(F,A,B) ),
inference(fof_nnf,[status(thm)],[thIIa14_neg]) ).
fof(sk_thIIa14_neg,plain,
( ~ equal_set(inverse_image2(sK0,empty_set),empty_set)
& maps(sK0,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3,sK4]),skolemize(F,sK0),skolemize(A,sK3),skolemize(B,sK4)],[nnf_29]) ).
cnf(c_302,negated_conjecture,
~ equal_set(inverse_image2(sK0,empty_set),empty_set),
inference(split_conjunct,[status(thm)],[sk_thIIa14_neg]) ).
fof(nnf_24,plain,
! [F,B,X] :
( ( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
| member(X,inverse_image2(F,B)) )
& ( ? [X0] :
( apply(F,X,X0)
& member(X0,B) )
| ~ member(X,inverse_image2(F,B)) ) ),
inference(fof_nnf,[status(thm)],[inverse_image2]) ).
fof(sk_inverse_image2_sk,plain,
! [F,B,X] :
( ( ! [Y] :
( ~ apply(F,X,Y)
| ~ member(Y,B) )
| member(X,inverse_image2(F,B)) )
& ( ( apply(F,X,sK1(F,B,X))
& member(sK1(F,B,X),B) )
| ~ member(X,inverse_image2(F,B)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(F,B,X))],[nnf_24]) ).
fof(sk_inverse_image2,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ apply(VAR_1,VAR_0,VAR_3)
| ~ member(VAR_3,VAR_2)
| member(VAR_0,inverse_image2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1,VAR_2] :
( apply(VAR_1,VAR_0,sK1(VAR_1,VAR_2,VAR_0))
| ~ member(VAR_0,inverse_image2(VAR_1,VAR_2)) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(sK1(VAR_1,VAR_2,VAR_0),VAR_2)
| ~ member(VAR_0,inverse_image2(VAR_1,VAR_2)) ) ),
inference(cnf_transformation,[status(thm)],[sk_inverse_image2_sk]) ).
cnf(c_312,plain,
( member(sK1(B,C,A),C)
| ~ member(A,inverse_image2(B,C)) ),
inference(split_conjunct,[status(thm)],[sk_inverse_image2]) ).
cnf(c_340,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set]) ).
cnf(c_349,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) ),
inference(clausify,[status(thm)],[equal_set]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK2(A,B),B)
& member(sK2(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X,sK2(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_sk]) ).
cnf(c_353,plain,
( member(sK2(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_1453,plain,
subset(empty_set,A),
inference(resolve,[status(thm)],[c_353,c_340]) ).
cnf(c_1470,plain,
( member(sK1(A,B,sK2(inverse_image2(A,B),C)),B)
| subset(inverse_image2(A,B),C) ),
inference(resolve,[status(thm)],[c_353,c_312]) ).
cnf(c_1783,plain,
( ~ subset(A,empty_set)
| equal_set(A,empty_set) ),
inference(resolve,[status(thm)],[c_1453,c_349]) ).
cnf(c_7063,plain,
subset(inverse_image2(A,empty_set),B),
inference(resolve,[status(thm)],[c_1470,c_340]) ).
cnf(c_7160,plain,
equal_set(inverse_image2(A,empty_set),empty_set),
inference(resolve,[status(thm)],[c_7063,c_1783]) ).
cnf(c_7161,plain,
$false,
inference(resolve,[status(thm)],[c_7160,c_302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET764+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 : Sat Sep 26 08:18:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 395996 was started by sandbox on n016,
% 0.09/0.37 % Sat Sep 26 08:18:01 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 72.69/10.62
% 72.69/10.62 % given #500 (I,wt=27): 619 -member(A,B) | apply(C,A,A) | -member(D,E) | -apply(F,A,D) | -apply(V6,D,A) | member(f11(C,V6,F,B,E,B),B). [factor(356,a,b)].
% 72.69/10.62
% 72.69/10.62 % given #1000 (I,wt=26): 1119 -member(A,B) | -member(C,B) | -apply(D,A,A) | -apply(D,A,C) | apply(E,A,C) | member(f29(D,B,D,B,E),B). [factor(696,d,e),merge(b)].
% 72.69/10.62
% 72.69/10.62 % SZS status Theorem for theBenchmark
% 72.69/10.62
% 72.69/10.62 % Proof 1 at 1.82 (+ 0.30) seconds.
% 72.69/10.62 % Length of proof is 16.
% 72.69/10.62 % Level of proof is 5.
% 72.69/10.62 % Maximum clause weight is 15.000.
% 72.69/10.62 % Given clauses 1496.
% 72.69/10.62
% 72.69/10.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------