%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU172+1 : 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 : n001.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 08:45:18 AM UTC 2026
% Result : Theorem 0.16s 10.67s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 11 unt; 0 def)
% Number of atoms : 36 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 12 ~; 4 |; 7 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 4 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(d5_subset_1,axiom,
! [A,B] :
( element(B,powerset(A))
=> subset_complement(A,B) = set_difference(A,B) ),
file('theBenchmark.p',d5_subset_1) ).
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(t54_subset_1,conjecture,
! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
file('theBenchmark.p',t54_subset_1) ).
fof(t54_subset_1_neg,negated_conjecture,
~ ! [A,B,C] :
( element(C,powerset(A))
=> ~ ( in(B,C)
& in(B,subset_complement(A,C)) ) ),
inference(assume_negation,[status(cth)],[t54_subset_1]) ).
cnf(c_23,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
cnf(c_40,plain,
( subset_complement(B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[d5_subset_1]) ).
cnf(c_42,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
fof(nnf_21,plain,
? [A,B,C] :
( in(B,C)
& in(B,subset_complement(A,C))
& element(C,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t54_subset_1_neg]) ).
fof(sk_t54_subset_1_neg,plain,
( in(sK2,sK0)
& in(sK2,subset_complement(sK1,sK0))
& element(sK0,powerset(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK0)],[nnf_21]) ).
cnf(c_47,negated_conjecture,
element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_t54_subset_1_neg]) ).
cnf(c_48,negated_conjecture,
in(sK2,subset_complement(sK1,sK0)),
inference(split_conjunct,[status(thm)],[sk_t54_subset_1_neg]) ).
cnf(c_49,negated_conjecture,
in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t54_subset_1_neg]) ).
cnf(c_92,plain,
subset_complement(sK1,sK0) = set_difference(sK1,sK0),
inference(resolve,[status(thm)],[c_47,c_40]) ).
cnf(c_95,negated_conjecture,
in(sK2,set_difference(sK1,sK0)),
inference(paramod,[status(thm)],[c_92,c_48]) ).
cnf(c_105,plain,
A = set_difference(A,empty_set),
inference(copy,[status(thm)],[c_23]) ).
cnf(c_106,plain,
( ~ in(A,C)
| ~ in(A,set_difference(set_difference(B,C),empty_set)) ),
inference(resolve,[status(thm)],[c_42,c_105]) ).
cnf(c_107,negated_conjecture,
~ in(sK2,set_difference(set_difference(A,sK0),empty_set)),
inference(resolve,[status(thm)],[c_106,c_49]) ).
cnf(c_103,negated_conjecture,
~ in(sK2,set_difference(A,sK0)),
inference(paramod,[status(thm)],[c_23,c_107]) ).
cnf(c_104,plain,
$false,
inference(resolve,[status(thm)],[c_103,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/10.64 % Computer : n001.cluster.edu
% 0.16/10.64 % Model : x86_64 x86_64
% 0.16/10.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/10.64 % Memory : 8046.5625MB
% 0.16/10.64 % OS : Linux 6.8.0-71-generic
% 0.16/10.64 % CPULimit : 300
% 0.16/10.64 % WCLimit : 300
% 0.16/10.64 % DateTime : Sat Sep 26 08:50:10 UTC 2026
% 0.16/10.64 % CPUTime :
% 0.16/10.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/10.65 % Process 1406676 was started by sandbox on n001,
% 0.16/10.65 % Sat Sep 26 08:50:10 2026
% 0.16/10.65 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/10.65
% 0.16/10.65 % From the command line: assign(max_seconds, 300).
% 0.16/10.67
% 0.16/10.67 % SZS status Theorem for theBenchmark
% 0.16/10.67
% 0.16/10.67 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.16/10.67 % Length of proof is 14.
% 0.16/10.67 % Level of proof is 4.
% 0.16/10.67 % Maximum clause weight is 11.000.
% 0.16/10.67 % Given clauses 26.
% 0.16/10.67
% 0.16/10.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------