%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET588+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 : 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 08:36:32 AM UTC 2026
% Result : Theorem 0.12s 5.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 20 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 25 !; 4 ?)
% 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(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(prove_difference_subset1,conjecture,
! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
file('theBenchmark.p',prove_difference_subset1) ).
fof(prove_difference_subset1_neg,negated_conjecture,
~ ! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
inference(assume_negation,[status(cth)],[prove_difference_subset1]) ).
fof(nnf_2,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(sK0(B,C),C)
& member(sK0(B,C),B) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(B,C))],[nnf_2]) ).
fof(sk_subset_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(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_5,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_6,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
cnf(c_7,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset_defn]) ).
fof(nnf_4,plain,
? [B,C,D] :
( ~ subset(difference(B,D),difference(C,D))
& subset(B,C) ),
inference(fof_nnf,[status(thm)],[prove_difference_subset1_neg]) ).
fof(sk_prove_difference_subset1_neg,plain,
( ~ subset(difference(sK1,sK3),difference(sK2,sK3))
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3)],[nnf_4]) ).
cnf(c_9,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_difference_subset1_neg]) ).
cnf(c_10,negated_conjecture,
~ subset(difference(sK1,sK3),difference(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_prove_difference_subset1_neg]) ).
cnf(c_11,negated_conjecture,
member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK1,sK3)),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_12,negated_conjecture,
~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),difference(sK2,sK3)),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_13,negated_conjecture,
( member(A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_16,plain,
( member(A,C)
| ~ member(A,B)
| member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_17,plain,
( ~ member(A,C)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_18,plain,
( member(A,B)
| ~ member(A,difference(B,C)) ),
inference(clausify,[status(thm)],[difference_defn]) ).
cnf(c_22,plain,
~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_24,plain,
member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK1),
inference(resolve,[status(thm)],[c_18,c_11]) ).
cnf(c_33,negated_conjecture,
( member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK3)
| ~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK2) ),
inference(resolve,[status(thm)],[c_16,c_12]) ).
cnf(c_28,negated_conjecture,
~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_34,negated_conjecture,
~ member(sK0(difference(sK1,sK3),difference(sK2,sK3)),sK1),
inference(resolve,[status(thm)],[c_13,c_28]) ).
cnf(c_32,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_24,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET588+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.37 % Computer : n020.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Sat Sep 26 07:58:56 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.38 % Process 1024570 was started by sandbox on n020,
% 0.12/5.38 % Sat Sep 26 07:58:56 2026
% 0.12/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/5.38
% 0.12/5.38 % From the command line: assign(max_seconds, 300).
% 0.12/5.39
% 0.12/5.39 % SZS status Theorem for theBenchmark
% 0.12/5.39
% 0.12/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/5.39 % Length of proof is 18.
% 0.12/5.39 % Level of proof is 5.
% 0.12/5.39 % Maximum clause weight is 11.000.
% 0.12/5.39 % Given clauses 12.
% 0.12/5.39
% 0.12/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------