%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU171+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 : n005.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 0.17s 5.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 70 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 32 ~; 13 |; 12 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_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(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(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t50_subset_1,conjecture,
! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
file('theBenchmark.p',t50_subset_1) ).
fof(t50_subset_1_neg,negated_conjecture,
~ ! [A] :
( A != empty_set
=> ! [B] :
( element(B,powerset(A))
=> ! [C] :
( element(C,A)
=> ( ~ in(C,B)
=> in(C,subset_complement(A,B)) ) ) ) ),
inference(assume_negation,[status(cth)],[t50_subset_1]) ).
cnf(c_24,plain,
( in(B,A)
| ~ element(B,A)
| empty(A) ),
inference(clausify,[status(thm)],[d2_subset_1]) ).
cnf(c_30,plain,
( in(D,B)
| ~ in(D,A)
| in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_34,plain,
( subset_complement(B,A) = set_difference(B,A)
| ~ element(A,powerset(B)) ),
inference(clausify,[status(thm)],[d5_subset_1]) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
cnf(c_38,plain,
empty(empty_set),
inference(clausify,[status(thm)],[fc1_xboole_0]) ).
cnf(c_50,plain,
( ~ empty(B)
| B = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t8_boole]) ).
fof(nnf_22,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(C,subset_complement(A,B))
& ~ in(C,B)
& element(C,A) )
& element(B,powerset(A)) )
& empty_set != A ),
inference(fof_nnf,[status(thm)],[t50_subset_1_neg]) ).
fof(sk_t50_subset_1_neg,plain,
( ~ in(sK2,subset_complement(sK0,sK1))
& ~ in(sK2,sK1)
& element(sK2,sK0)
& element(sK1,powerset(sK0))
& empty_set != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_22]) ).
cnf(c_51,negated_conjecture,
empty_set != sK0,
inference(split_conjunct,[status(thm)],[sk_t50_subset_1_neg]) ).
cnf(c_52,negated_conjecture,
sK0 != empty_set,
inference(copy,[status(thm)],[c_51]) ).
cnf(c_53,negated_conjecture,
element(sK1,powerset(sK0)),
inference(split_conjunct,[status(thm)],[sk_t50_subset_1_neg]) ).
cnf(c_54,negated_conjecture,
element(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_t50_subset_1_neg]) ).
cnf(c_55,negated_conjecture,
~ in(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t50_subset_1_neg]) ).
cnf(c_56,negated_conjecture,
~ in(sK2,subset_complement(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t50_subset_1_neg]) ).
cnf(c_214,plain,
( ~ empty(A)
| A = empty_set ),
inference(resolve,[status(thm)],[c_50,c_38]) ).
cnf(c_130,negated_conjecture,
~ empty(sK0),
inference(resolve,[status(thm)],[c_214,c_52]) ).
cnf(c_133,plain,
subset_complement(sK0,sK1) = set_difference(sK0,sK1),
inference(resolve,[status(thm)],[c_53,c_34]) ).
cnf(c_215,negated_conjecture,
( in(sK2,sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_54,c_24]) ).
cnf(c_135,negated_conjecture,
in(sK2,sK0),
inference(resolve,[status(thm)],[c_130,c_215]) ).
cnf(c_216,negated_conjecture,
( in(sK2,B)
| ~ in(sK2,A)
| set_difference(A,B) != subset_complement(sK0,sK1) ),
inference(resolve,[status(thm)],[c_30,c_56]) ).
cnf(c_217,negated_conjecture,
( in(sK2,A)
| set_difference(sK0,A) != subset_complement(sK0,sK1) ),
inference(resolve,[status(thm)],[c_216,c_135]) ).
cnf(c_218,negated_conjecture,
set_difference(sK0,sK1) != subset_complement(sK0,sK1),
inference(resolve,[status(thm)],[c_217,c_55]) ).
cnf(c_219,negated_conjecture,
subset_complement(sK0,sK1) != set_difference(sK0,sK1),
inference(copy,[status(thm)],[c_218]) ).
cnf(c_213,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_133,c_219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU171+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.42 % Computer : n005.cluster.edu
% 0.17/5.42 % Model : x86_64 x86_64
% 0.17/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.42 % Memory : 8046.5625MB
% 0.17/5.42 % OS : Linux 6.8.0-71-generic
% 0.17/5.42 % CPULimit : 300
% 0.17/5.42 % WCLimit : 300
% 0.17/5.42 % DateTime : Sat Sep 26 08:44:23 UTC 2026
% 0.17/5.42 % CPUTime :
% 0.17/5.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.42 % Process 1729937 was started by sandbox2 on n005,
% 0.17/5.42 % Sat Sep 26 08:44:23 2026
% 0.17/5.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.43
% 0.17/5.43 % From the command line: assign(max_seconds, 300).
% 0.17/5.45
% 0.17/5.45 % SZS status Theorem for theBenchmark
% 0.17/5.45
% 0.17/5.45 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/5.45 % Length of proof is 20.
% 0.17/5.45 % Level of proof is 5.
% 0.17/5.45 % Maximum clause weight is 24.000.
% 0.17/5.45 % Given clauses 48.
% 0.17/5.45
% 0.17/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------