TSTP Solution File: SET580+3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET580+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:53:36 EDT 2023
% Result : Theorem 3.47s 1.81s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 20 ( 7 unt; 4 typ; 0 def)
% Number of atoms : 54 ( 9 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 187 ( 9 ~; 3 |; 11 &; 140 @)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(difference_type,type,
difference: $i > $i > $i ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( symmetric_difference @ B @ C ) )
<=> ~ ( ( member @ A @ B )
<=> ( member @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th23) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( member @ A @ ( symmetric_difference @ B @ C ) )
<=> ~ ( ( member @ A @ B )
<=> ( member @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( member @ A @ ( symmetric_difference @ B @ C ) )
=> ~ ( ( ( member @ A @ B )
=> ( member @ A @ C ) )
& ( ( member @ A @ C )
=> ( member @ A @ B ) ) ) )
& ( ~ ( ( ( member @ A @ B )
=> ( member @ A @ C ) )
& ( ( member @ A @ C )
=> ( member @ A @ B ) ) )
=> ( member @ A @ ( symmetric_difference @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( member @ C @ A )
<=> ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( ( member @ C @ A )
=> ( member @ C @ B ) )
& ( ( member @ C @ B )
=> ( member @ C @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference_defn) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( union @ ( difference @ A @ B ) @ ( difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( union @ A @ B )
= ( union @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( difference @ A @ B ) )
<=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( difference @ A @ B ) )
=> ( ( member @ C @ A )
& ~ ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
& ~ ( member @ C @ B ) )
=> ( member @ C @ ( difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( member @ C @ ( union @ A @ B ) )
<=> ( ( member @ C @ A )
| ( member @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
thf(19,plain,
! [A: $i,B: $i,C: $i] :
( ( ( member @ C @ ( union @ A @ B ) )
=> ( ( member @ C @ A )
| ( member @ C @ B ) ) )
& ( ( ( member @ C @ A )
| ( member @ C @ B ) )
=> ( member @ C @ ( union @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(73,plain,
$false,
inference(e,[status(thm)],[38,9,41,32,35,26,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET580+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:09:44 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.01 % [INFO] Parsing done (127ms).
% 1.33/1.02 % [INFO] Running in sequential loop mode.
% 1.72/1.22 % [INFO] eprover registered as external prover.
% 1.72/1.22 % [INFO] cvc4 registered as external prover.
% 1.72/1.22 % [INFO] Scanning for conjecture ...
% 1.77/1.27 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.77/1.29 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.77/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.77/1.31 % [INFO] Type checking passed.
% 1.77/1.31 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.47/1.81 % External prover 'e' found a proof!
% 3.47/1.81 % [INFO] Killing All external provers ...
% 3.47/1.81 % Time passed: 1301ms (effective reasoning time: 785ms)
% 3.47/1.81 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.47/1.81 % Axioms used in derivation (6): equal_member_defn, symmetric_difference_defn, commutativity_of_symmetric_difference, union_defn, difference_defn, commutativity_of_union
% 3.47/1.81 % No. of inferences in proof: 16
% 3.47/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1301 ms resp. 785 ms w/o parsing
% 3.47/1.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.47/1.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------