TSTP Solution File: SWV284-2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SWV284-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Tue May 21 05:51:06 EDT 2024
% Result : Unsatisfiable 7.15s 2.45s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 14 unt; 15 typ; 0 def)
% Number of atoms : 66 ( 6 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 416 ( 30 ~; 20 |; 0 &; 366 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 68 ( 0 ^ 68 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_x_type,type,
v_x: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
thf(v_list_type,type,
v_list: $i ).
thf(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
thf(v_N_type,type,
v_N: $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_msg_type,type,
v_msg: $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(v_sko__upX_type,type,
v_sko__upX: $i > $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
! [A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
inference(cnf,[status(esa)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
! [A: $i] : ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_0) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(cnf,[status(esa)],[14]) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ C @ D @ tc_nat )
| ( ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat )
!= ( c_lessequals @ ( c_plus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[7,15]) ).
thf(54,plain,
! [B: $i,A: $i] : ( c_lessequals @ B @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( c_plus @ I @ J @ tc_nat )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( v_x @ ( c_plus @ I @ J @ tc_nat ) ))]]) ).
thf(55,plain,
! [B: $i,A: $i] : ( c_lessequals @ B @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(simp,[status(thm)],[54]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg__Nonce__supply_0) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__upX @ B ) @ A @ tc_nat ) ),
inference(cnf,[status(esa)],[12]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Message_Oparts @ ( c_insert @ D @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( ( c_lessequals @ B @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat )
!= ( c_lessequals @ ( v_sko__upX @ D ) @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[55,13]) ).
thf(60,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ B ) @ tc_nat ) ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( G )),bind(B,$thf( v_sko__upX @ J )),bind(C,$thf( v_x @ ( c_plus @ G @ ( v_sko__upX @ J ) @ tc_nat ) )),bind(D,$thf( J ))]]) ).
thf(67,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ B ) @ tc_nat ) ) ) @ ( c_Message_Oparts @ ( c_insert @ B @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ),
inference(simp,[status(thm)],[60]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ A ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
!= ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ B @ ( v_sko__upX @ C ) @ tc_nat ) ) ) @ ( c_Message_Oparts @ ( c_insert @ C @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) ),
inference(paramod_ordered,[status(thm)],[11,67]) ).
thf(188,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ v_msg ) @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( c_plus @ D @ ( v_sko__upX @ v_msg ) @ tc_nat )),bind(B,$thf( D )),bind(C,$thf( v_msg ))]]) ).
thf(191,plain,
! [A: $i] : ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ v_msg ) @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
inference(simp,[status(thm)],[188]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ C @ tc_nat )
| ( c_lessequals @ A @ C @ tc_nat ) ),
inference(cnf,[status(esa)],[16]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ B @ D @ tc_nat )
| ( ( c_lessequals @ A @ ( v_x @ A ) @ tc_nat )
!= ( c_lessequals @ ( c_plus @ B @ C @ tc_nat ) @ D @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[7,17]) ).
thf(93,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( c_plus @ I @ J @ tc_nat )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( v_x @ ( c_plus @ I @ J @ tc_nat ) ))]]) ).
thf(97,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat ),
inference(simp,[status(thm)],[93]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ A ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_N @ A @ tc_nat ) ),
inference(cnf,[status(esa)],[8]) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ C ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
| ( ( c_lessequals @ A @ ( v_x @ ( c_plus @ A @ B @ tc_nat ) ) @ tc_nat )
!= ( c_lessequals @ v_N @ C @ tc_nat ) ) ),
inference(paramod_ordered,[status(thm)],[97,10]) ).
thf(100,plain,
! [A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ v_N @ A @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( v_N )),bind(B,$thf( F )),bind(C,$thf( v_x @ ( c_plus @ v_N @ F @ tc_nat ) ))]]) ).
thf(109,plain,
! [A: $i] :
~ ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ v_N @ A @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ),
inference(simp,[status(thm)],[100]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ A @ ( v_sko__upX @ v_msg ) @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg )
!= ( c_in @ ( c_Message_Omsg_ONonce @ ( v_x @ ( c_plus @ v_N @ B @ tc_nat ) ) ) @ ( c_Event_Oused @ v_list ) @ tc_Message_Omsg ) ),
inference(paramod_ordered,[status(thm)],[191,109]) ).
thf(210,plain,
$false,
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( v_N )),bind(B,$thf( v_sko__upX @ v_msg ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV284-2 : TPTP v8.2.0. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n006.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 07:48:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (101ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.61/1.17 % [INFO] nitpick registered as external prover.
% 1.61/1.18 % [INFO] Scanning for conjecture ...
% 1.79/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.79/1.26 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.79/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.79/1.27 % [INFO] Type checking passed.
% 1.79/1.27 % [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 ...
% 7.15/2.44 % [INFO] Killing All external provers ...
% 7.15/2.45 % Time passed: 1923ms (effective reasoning time: 1477ms)
% 7.15/2.45 % Axioms used in derivation (3): cls_Nat_Oadd__leE_0, cls_Message_Omsg__Nonce__supply_0, cls_Nat_Oadd__leE_1
% 7.15/2.45 % No. of inferences in proof: 34
% 7.15/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1923 ms resp. 1477 ms w/o parsing
% 7.15/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.15/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------