%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU133+2 : TPTP v9.3.1. Released v3.3.0.
% 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 08:45:07 AM UTC 2026
% Result : Theorem 6.55s 1.25s
% Output : CNFRefutation 6.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 56 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 50 ( 22 ~; 16 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 8 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
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(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
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]) ).
cnf(c_47,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(nnf_7,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_7]) ).
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_61,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_62,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_69,plain,
( in(D,A)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_94,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_110,plain,
subset(A,set_union2(A,B)),
inference(clausify,[status(thm)],[t7_xboole_1]) ).
fof(nnf_45,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_45]) ).
cnf(c_113,negated_conjecture,
~ subset(set_difference(sK1,sK2),sK1),
inference(split_conjunct,[status(thm)],[sk_t36_xboole_1_neg]) ).
cnf(c_668,plain,
subset(A,set_union2(B,A)),
inference(paramod,[status(thm)],[c_47,c_110]) ).
cnf(c_677,plain,
in(sK0(set_difference(sK1,sK2),sK1),set_difference(sK1,sK2)),
inference(resolve,[status(thm)],[c_113,c_61]) ).
cnf(c_682,negated_conjecture,
~ in(sK0(set_difference(sK1,sK2),sK1),sK1),
inference(resolve,[status(thm)],[c_62,c_113]) ).
cnf(c_967,plain,
set_intersection2(A,set_union2(B,A)) = A,
inference(resolve,[status(thm)],[c_668,c_94]) ).
cnf(c_4840,plain,
A = set_intersection2(A,set_union2(B,A)),
inference(copy,[status(thm)],[c_967]) ).
cnf(c_4841,plain,
( in(A,B)
| ~ in(A,set_intersection2(set_difference(B,C),set_union2(D,set_difference(B,C)))) ),
inference(resolve,[status(thm)],[c_69,c_4840]) ).
cnf(c_4842,plain,
~ in(sK0(set_difference(sK1,sK2),sK1),set_intersection2(set_difference(sK1,A),set_union2(B,set_difference(sK1,A)))),
inference(resolve,[status(thm)],[c_4841,c_682]) ).
cnf(c_4838,plain,
~ in(sK0(set_difference(sK1,sK2),sK1),set_difference(sK1,A)),
inference(paramod,[status(thm)],[c_967,c_4842]) ).
cnf(c_4839,plain,
$false,
inference(resolve,[status(thm)],[c_4838,c_677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU133+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:38:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 160707 was started by sandbox on n012,
% 0.08/0.36 % Sat Sep 26 08:38:19 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 6.55/1.25
% 6.55/1.25 % SZS status Theorem for theBenchmark
% 6.55/1.25
% 6.55/1.25 % Proof 1 at 0.61 (+ 0.26) seconds.
% 6.55/1.25 % Length of proof is 19.
% 6.55/1.25 % Level of proof is 5.
% 6.55/1.25 % Maximum clause weight is 11.000.
% 6.55/1.25 % Given clauses 314.
% 6.55/1.25
% 6.55/1.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------