%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU132+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 : n010.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 32.78s 4.58s
% Output : CNFRefutation 32.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 71 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 75 ( 33 ~; 27 |; 9 &)
% ( 3 <=>; 3 =>; 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 : 59 ( 4 sgn 26 !; 4 ?)
% 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(t33_xboole_1,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('theBenchmark.p',t33_xboole_1) ).
fof(t33_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
inference(assume_negation,[status(cth)],[t33_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_16,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
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_20,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_21,plain,
( in(D,B)
| ~ in(D,A)
| in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
fof(nnf_14,plain,
? [A,B,C] :
( ~ subset(set_difference(A,C),set_difference(B,C))
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t33_xboole_1_neg]) ).
fof(sk_t33_xboole_1_neg,plain,
( ~ subset(set_difference(sK1,sK3),set_difference(sK2,sK3))
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_14]) ).
cnf(c_34,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t33_xboole_1_neg]) ).
cnf(c_35,negated_conjecture,
~ subset(set_difference(sK1,sK3),set_difference(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_t33_xboole_1_neg]) ).
cnf(c_42,plain,
( in(A,B)
| ~ in(A,set_difference(B,C)) ),
inference(xxres,[status(thm)],[c_19]) ).
cnf(c_43,plain,
( ~ in(A,C)
| ~ in(A,set_difference(B,C)) ),
inference(xxres,[status(thm)],[c_20]) ).
cnf(c_44,plain,
( in(A,C)
| ~ in(A,B)
| in(A,set_difference(B,C)) ),
inference(xxres,[status(thm)],[c_21]) ).
cnf(c_79,plain,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_34,c_16]) ).
cnf(c_80,plain,
in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),set_difference(sK1,sK3)),
inference(resolve,[status(thm)],[c_35,c_17]) ).
cnf(c_81,negated_conjecture,
~ in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),set_difference(sK2,sK3)),
inference(resolve,[status(thm)],[c_18,c_35]) ).
cnf(c_365,plain,
~ in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),sK3),
inference(resolve,[status(thm)],[c_80,c_43]) ).
cnf(c_366,plain,
in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),sK1),
inference(resolve,[status(thm)],[c_80,c_42]) ).
cnf(c_8703,plain,
( in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),sK3)
| ~ in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),sK2) ),
inference(resolve,[status(thm)],[c_44,c_81]) ).
cnf(c_8509,plain,
~ in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_8703,c_365]) ).
cnf(c_8704,plain,
in(sK0(set_difference(sK1,sK3),set_difference(sK2,sK3)),sK2),
inference(resolve,[status(thm)],[c_366,c_79]) ).
cnf(c_8702,plain,
$false,
inference(resolve,[status(thm)],[c_8509,c_8704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU132+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 08:39:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2930407 was started by sandbox2 on n010,
% 0.10/0.36 % Sat Sep 26 08:39:00 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 32.78/4.58
% 32.78/4.58 % given #500 (T,wt=15): 5337 set_difference(c3,c4) = empty_set. [resolve(284,b,23,c),merge(b),unit_del(b,73)].
% 32.78/4.58
% 32.78/4.58 % SZS status Theorem for theBenchmark
% 32.78/4.58
% 32.78/4.58 % Proof 1 at 3.11 (+ 1.04) seconds.
% 32.78/4.58 % Length of proof is 21.
% 32.78/4.58 % Level of proof is 5.
% 32.78/4.58 % Maximum clause weight is 26.000.
% 32.78/4.58 % Given clauses 766.
% 32.78/4.58
% 32.78/4.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------