TSTP Solution File: SWV249-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV249-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 12:14:30 EDT 2023
% Result : Unsatisfiable 3.73s 2.00s
% Output : Refutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 30
% Syntax : Number of formulae : 48 ( 19 unt; 13 typ; 0 def)
% Number of atoms : 57 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 394 ( 24 ~; 22 |; 0 &; 348 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 92 ( 0 ^; 92 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_X_type,type,
v_X: $i ).
thf(c_Message_Osynth_type,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_type,type,
c_Message_Oanalz: $i > $i ).
thf(v_G_type,type,
v_G: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(v_H_type,type,
v_H: $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__synth__Un_0) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Osynth @ A ) @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_minus @ B @ A @ ( tc_set @ C ) ) @ C )
= ( c_union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_union @ D @ A @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oanalz @ B ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ A @ ( c_insert @ B @ C @ D ) @ D )
= ( c_insert @ B @ ( c_union @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(18,plain,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_union @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ C )
= ( c_union @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( c_union @ ( c_minus @ A @ B @ ( tc_set @ C ) ) @ B @ C )
= ( c_union @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ A @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(19,plain,
~ ( c_lessequals @ ( c_Message_Oanalz @ ( c_insert @ v_X @ v_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_G ) ) @ ( c_Message_Oanalz @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_union @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__analz__Un_0) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( c_Message_Oanalz @ ( c_union @ ( c_Message_Oanalz @ A ) @ B @ tc_Message_Omsg ) )
= ( c_Message_Oanalz @ ( c_union @ A @ B @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_insert @ A @ B @ C ) @ D @ ( tc_set @ C ) )
| ( c_lessequals @ B @ D @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_insert @ A @ D @ C ) @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(17,axiom,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(50,plain,
! [A: $i] : ( class_Orderings_Oorder @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_union @ ( c_insert @ A @ B @ C ) @ D @ C )
= ( c_insert @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(62,plain,
$false,
inference(e,[status(thm)],[29,41,45,27,39,35,18,43,23,19,47,37,25,21,33,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV249-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n009.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 02:15:18 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.93/0.93 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.07 % [INFO] Parsing done (139ms).
% 1.37/1.08 % [INFO] Running in sequential loop mode.
% 1.80/1.29 % [INFO] eprover registered as external prover.
% 1.80/1.30 % [INFO] cvc4 registered as external prover.
% 1.80/1.30 % [INFO] Scanning for conjecture ...
% 1.97/1.36 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 2.08/1.40 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.08/1.42 % [INFO] Problem is propositional (TPTP CNF).
% 2.08/1.43 % [INFO] Type checking passed.
% 2.08/1.43 % [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 ...
% 3.73/1.99 % External prover 'e' found a proof!
% 3.73/1.99 % [INFO] Killing All external provers ...
% 3.73/1.99 % Time passed: 1438ms (effective reasoning time: 913ms)
% 3.73/1.99 % 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)>
% 3.73/1.99 % Axioms used in derivation (15): cls_Message_Oanalz__synth__Un_0, cls_Set_OUn__Diff__cancel2_0, cls_Set_Oinsert__subset_2, cls_Set_OUn__subset__iff_0, cls_Set_Osubset__antisym_0, cls_Set_OUn__insert__left_0, cls_Set_OUn__insert__right_0, cls_Message_Oanalz__analz__Un_0, cls_Set_OUn__subset__iff_1, cls_Set_OUn__subset__iff_2, clsarity_set_2, cls_Message_Oanalz__mono_0, cls_Set_Oinsert__subset_1, cls_Set_OUn__Diff__cancel_0, cls_Orderings_Oorder__class_Oaxioms__1_0
% 3.73/1.99 % No. of inferences in proof: 35
% 3.73/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1438 ms resp. 913 ms w/o parsing
% 3.73/2.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.73/2.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------