%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU133+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:45:07 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 48 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 47 ( 21 ~; 15 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 4 sgn 25 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t36_xboole_1,conjecture,
! [A,B] : subset(set_difference(A,B),A),
file('theBenchmark.p',t36_xboole_1) ).
fof(t36_xboole_1_neg,negated_conjecture,
~ ! [A,B] : subset(set_difference(A,B),A),
inference(assume_negation,[status(cth)],[t36_xboole_1]) ).
fof(nnf_2,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_2]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_17,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_18,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_19,plain,
( in(D,A)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_29,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
fof(nnf_14,plain,
? [A,B] : ~ subset(set_difference(A,B),A),
inference(fof_nnf,[status(thm)],[t36_xboole_1_neg]) ).
fof(sk_t36_xboole_1_neg,plain,
~ subset(set_difference(sK1,sK2),sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_14]) ).
cnf(c_34,negated_conjecture,
~ subset(set_difference(sK1,sK2),sK1),
inference(split_conjunct,[status(thm)],[sk_t36_xboole_1_neg]) ).
cnf(c_66,plain,
in(sK0(set_difference(sK1,sK2),sK1),set_difference(sK1,sK2)),
inference(resolve,[status(thm)],[c_34,c_17]) ).
cnf(c_67,negated_conjecture,
~ in(sK0(set_difference(sK1,sK2),sK1),sK1),
inference(resolve,[status(thm)],[c_18,c_34]) ).
cnf(c_90,plain,
A = set_difference(A,empty_set),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_91,plain,
( in(A,B)
| ~ in(A,set_difference(set_difference(B,C),empty_set)) ),
inference(resolve,[status(thm)],[c_19,c_90]) ).
cnf(c_92,plain,
~ in(sK0(set_difference(sK1,sK2),sK1),set_difference(set_difference(sK1,A),empty_set)),
inference(resolve,[status(thm)],[c_91,c_67]) ).
cnf(c_88,plain,
~ in(sK0(set_difference(sK1,sK2),sK1),set_difference(sK1,A)),
inference(paramod,[status(thm)],[c_29,c_92]) ).
cnf(c_89,plain,
$false,
inference(resolve,[status(thm)],[c_88,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU133+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 08:38:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1264238 was started by sandbox2 on n004,
% 0.09/0.36 % Sat Sep 26 08:38:36 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 13.
% 0.09/0.40 % Level of proof is 4.
% 0.09/0.40 % Maximum clause weight is 11.000.
% 0.09/0.40 % Given clauses 29.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------