TSTP Solution File: SWV276-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV276-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 12:14:43 EDT 2023
% Result : Unsatisfiable 3.27s 1.85s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 37
% Syntax : Number of formulae : 57 ( 21 unt; 18 typ; 0 def)
% Number of atoms : 65 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 378 ( 24 ~; 26 |; 0 &; 328 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 70 ( 0 ^; 70 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_K_type,type,
v_K: $i ).
thf(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(v_X_type,type,
v_X: $i ).
thf(v_G_type,type,
v_G: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(tc_nat_type,type,
tc_nat: $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_H_type,type,
v_H: $i ).
thf(c_union_type,type,
c_union: $i > $i > $i > $i ).
thf(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Message_OinvKey_type,type,
c_Message_OinvKey: $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(v_sko__uhi_type,type,
v_sko__uhi: $i > $i > $i ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_union @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D )
| ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,negated_conjecture,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_G @ tc_Message_Omsg ) ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(20,plain,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_G @ tc_Message_Omsg ) ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( c_Message_OkeysFor @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(41,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ A ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Osynth @ A ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(45,plain,
! [A: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,negated_conjecture,
~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(22,plain,
~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ B @ A ) ) @ B @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ B @ A ) ) @ B @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_Oanalz @ B ) @ tc_Message_Omsg )
| ( c_in @ A @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(31,plain,
! [A: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ A ) )
= ( c_Message_Oparts @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_set @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( c_Message_Oparts @ ( c_union @ A @ B @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ A ) @ ( c_Message_Oparts @ B ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ A @ C @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__subset__Un_0) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ tc_Message_Omsg )
| ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ A @ C @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ B ) @ ( c_Message_Oparts @ C ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( A
= ( c_Message_OinvKey @ ( v_sko__uhi @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ B ) ) @ tc_nat )
| ( c_in @ A @ ( c_Message_OkeysFor @ B ) @ tc_nat )
| ( A
= ( c_Message_OinvKey @ ( v_sko__uhi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(21,plain,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ ( c_union @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ ( tc_set @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__mono_0) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ A ) @ ( c_Message_OkeysFor @ B ) @ ( tc_set @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
thf(55,plain,
! [A: $i] : ( c_lessequals @ ( c_Message_Oanalz @ A ) @ ( c_Message_Oparts @ A ) @ ( tc_set @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(23,plain,
~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(59,plain,
$false,
inference(e,[status(thm)],[37,20,53,41,45,22,49,39,35,31,43,51,47,28,21,33,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV276-2 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 03:03:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.04 % [INFO] Parsing done (141ms).
% 1.41/1.04 % [INFO] Running in sequential loop mode.
% 1.81/1.27 % [INFO] eprover registered as external prover.
% 1.81/1.28 % [INFO] cvc4 registered as external prover.
% 1.81/1.28 % [INFO] Scanning for conjecture ...
% 1.98/1.35 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 2.09/1.40 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.09/1.43 % [INFO] Problem is propositional (TPTP CNF).
% 2.09/1.43 % [INFO] Type checking passed.
% 2.09/1.44 % [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 ...
% 3.27/1.84 % External prover 'e' found a proof!
% 3.27/1.84 % [INFO] Killing All external provers ...
% 3.27/1.84 % Time passed: 1321ms (effective reasoning time: 797ms)
% 3.27/1.84 % 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)>
% 3.27/1.85 % Axioms used in derivation (15): cls_Message_OkeysFor__Un_0, cls_Message_Oanalz__conj__parts_0, cls_Message_Oparts__synth_0, cls_Set_OUn__iff_0, cls_Set_OsubsetD_0, cls_Set_OUn__iff_1, cls_Message_Oanalz__subset__parts_0, cls_Event_OkeysFor__synth_H_1, cls_Message_Oparts__analz_0, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_Message_Oparts__insert__subset__Un_0, cls_Event_OkeysFor__synth_H_0, cls_Message_Oparts__Un_0, cls_Set_OUn__iff_2, cls_Message_OkeysFor__mono_0
% 3.27/1.85 % No. of inferences in proof: 39
% 3.27/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1321 ms resp. 797 ms w/o parsing
% 3.60/1.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.60/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------