%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET603+3 : 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 : n012.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 08:36:35 AM UTC 2026
% Result : Theorem 0.99s 0.50s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 14 unt; 0 def)
% Number of atoms : 63 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 22 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 3 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',difference_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(equal_defn,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('theBenchmark.p',equal_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_th74,conjecture,
! [B] : difference(B,empty_set) = B,
file('theBenchmark.p',prove_th74) ).
fof(prove_th74_neg,negated_conjecture,
~ ! [B] : difference(B,empty_set) = B,
inference(assume_negation,[status(cth)],[prove_th74]) ).
fof(nnf_9,plain,
? [B] : difference(B,empty_set) != B,
inference(fof_nnf,[status(thm)],[prove_th74_neg]) ).
fof(sk_prove_th74_neg,plain,
difference(sK0,empty_set) != sK0,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B,sK0)],[nnf_9]) ).
cnf(c_13,negated_conjecture,
difference(sK0,empty_set) != sK0,
inference(split_conjunct,[status(thm)],[sk_prove_th74_neg]) ).
fof(nnf_6,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(fof_nnf,[status(thm)],[subset_defn]) ).
fof(sk_subset_defn_sk,plain,
! [B,C] :
( ( ( ~ member(sK1(B,C),C)
& member(sK1(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(D,sK1(B,C))],[nnf_6]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK1(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK1(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_defn_sk]) ).
cnf(c_15,plain,
( ~ member(sK1(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_16,plain,
( member(sK1(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_22,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[equal_defn]) ).
cnf(c_25,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
cnf(c_26,plain,
( member(A,C)
| ~ member(A,B)
| member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_28,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_54,plain,
( subset(A,B)
| member(sK1(A,B),C)
| member(sK1(A,B),difference(A,C)) ),
inference(resolve,[status(thm)],[c_26,c_16]) ).
cnf(c_842,plain,
( subset(A,B)
| member(sK1(A,B),difference(A,empty_set)) ),
inference(resolve,[status(thm)],[c_54,c_25]) ).
cnf(c_1037,plain,
( subset(A,difference(A,empty_set))
| subset(A,difference(A,empty_set)) ),
inference(resolve,[status(thm)],[c_842,c_15]) ).
cnf(c_875,plain,
subset(A,difference(A,empty_set)),
inference(copy,[status(thm)],[c_1037]) ).
cnf(c_1038,negated_conjecture,
sK0 != difference(sK0,empty_set),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_1039,negated_conjecture,
( ~ subset(sK0,difference(sK0,empty_set))
| ~ subset(difference(sK0,empty_set),sK0) ),
inference(resolve,[status(thm)],[c_22,c_1038]) ).
cnf(c_891,negated_conjecture,
~ subset(difference(sK0,empty_set),sK0),
inference(resolve,[status(thm)],[c_1039,c_875]) ).
cnf(c_949,plain,
member(sK1(difference(sK0,empty_set),sK0),difference(sK0,empty_set)),
inference(resolve,[status(thm)],[c_891,c_16]) ).
cnf(c_963,plain,
~ member(sK1(difference(sK0,empty_set),sK0),sK0),
inference(resolve,[status(thm)],[c_15,c_891]) ).
cnf(c_1035,plain,
~ member(sK1(difference(sK0,empty_set),sK0),difference(sK0,A)),
inference(resolve,[status(thm)],[c_28,c_963]) ).
cnf(c_1036,plain,
$false,
inference(resolve,[status(thm)],[c_1035,c_949]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET603+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 07:58:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 73787 was started by sandbox on n012,
% 0.08/0.35 % Sat Sep 26 07:58:35 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.99/0.50
% 0.99/0.50 % SZS status Theorem for theBenchmark
% 0.99/0.50
% 0.99/0.50 % Proof 1 at 0.09 (+ 0.05) seconds.
% 0.99/0.50 % Length of proof is 20.
% 0.99/0.50 % Level of proof is 8.
% 0.99/0.50 % Maximum clause weight is 25.000.
% 0.99/0.50 % Given clauses 102.
% 0.99/0.50
% 0.99/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------