%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU172+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 : n003.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 0.13s 5.56s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 13 unt; 0 def)
% Number of atoms : 50 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 9 |; 7 &)
% ( 3 <=>; 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(t40_xboole_1,axiom,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
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]) ).
fof(nnf_110,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(sK0,sK1)
& in(sK0,subset_complement(sK2,sK1))
& element(sK1,powerset(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0]),skolemize(A,sK2),skolemize(B,sK0),skolemize(C,sK1)],[nnf_110]) ).
cnf(c_111,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t54_subset_1_neg]) ).
cnf(c_112,negated_conjecture,
in(sK0,subset_complement(sK2,sK1)),
inference(split_conjunct,[status(thm)],[sk_t54_subset_1_neg]) ).
cnf(c_113,negated_conjecture,
element(sK1,powerset(sK2)),
inference(split_conjunct,[status(thm)],[sk_t54_subset_1_neg]) ).
cnf(c_130,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_131,plain,
( in(B,A)
| set_difference(A,singleton(B)) = A ),
inference(clausify,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_132,plain,
( in(B,A)
| set_difference(A,unordered_pair(B,B)) = A ),
inference(paramod,[status(thm)],[c_130,c_131]) ).
cnf(c_133,plain,
( ~ in(B,A)
| set_difference(A,singleton(B)) != A ),
inference(clausify,[status(thm)],[t65_zfmisc_1]) ).
cnf(c_134,plain,
( ~ in(B,A)
| set_difference(A,unordered_pair(B,B)) != A ),
inference(paramod,[status(thm)],[c_130,c_133]) ).
cnf(c_148,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(clausify,[status(thm)],[t40_xboole_1]) ).
cnf(c_243,plain,
( subset_complement(B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[d5_subset_1]) ).
cnf(c_248,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_386,plain,
set_difference(subset_complement(sK2,sK1),unordered_pair(sK0,sK0)) != subset_complement(sK2,sK1),
inference(resolve,[status(thm)],[c_134,c_112]) ).
cnf(c_777,plain,
subset_complement(sK2,sK1) = set_difference(sK2,sK1),
inference(resolve,[status(thm)],[c_243,c_113]) ).
cnf(c_1029,plain,
set_difference(set_difference(sK2,sK1),unordered_pair(sK0,sK0)) != subset_complement(sK2,sK1),
inference(paramod,[status(thm)],[c_777,c_386]) ).
cnf(c_827,plain,
set_difference(set_difference(sK2,sK1),unordered_pair(sK0,sK0)) != set_difference(sK2,sK1),
inference(paramod,[status(thm)],[c_777,c_1029]) ).
cnf(c_1030,plain,
( ~ in(A,C)
| ~ in(A,set_difference(B,C)) ),
inference(resolve,[status(thm)],[c_248,c_148]) ).
cnf(c_1031,plain,
( set_difference(set_difference(C,B),unordered_pair(A,A)) = set_difference(C,B)
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_1030,c_132]) ).
cnf(c_1027,negated_conjecture,
set_difference(set_difference(A,sK1),unordered_pair(sK0,sK0)) = set_difference(A,sK1),
inference(resolve,[status(thm)],[c_1031,c_111]) ).
cnf(c_1028,plain,
$false,
inference(resolve,[status(thm)],[c_1027,c_827]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 08:46:00 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.37 % Process 2479598 was started by sandbox on n003,
% 0.09/5.37 % Sat Sep 26 08:46:00 2026
% 0.09/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/5.40
% 0.09/5.40 % From the command line: assign(max_seconds, 300).
% 0.13/5.56
% 0.13/5.56 % SZS status Theorem for theBenchmark
% 0.13/5.56
% 0.13/5.56 % Proof 1 at 0.11 (+ 0.04) seconds.
% 0.13/5.56 % Length of proof is 22.
% 0.13/5.56 % Level of proof is 5.
% 0.13/5.56 % Maximum clause weight is 31.000.
% 0.13/5.56 % Given clauses 95.
% 0.13/5.56
% 0.13/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------