TSTP Solution File: SET844-2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET844-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 03:07:09 EDT 2024
% Result : Unsatisfiable 4.82s 2.38s
% Output : Refutation 4.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 38 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 62 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 423 ( 30 ~; 27 |; 0 &; 366 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 0 ^ 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_m_type,type,
v_m: $i ).
thf(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(v_S_type,type,
v_S: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(4,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(12,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
| ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
| ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) )
| ( c_in @ ( c_Union @ A @ ( tc_set @ C ) ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(23,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Union @ C @ ( tc_set @ E ) ) @ ( c_Zorn_OTFin @ D @ E ) @ ( tc_set @ ( tc_set @ E ) ) )
| ( ( c_lessequals @ A @ A @ ( tc_set @ B ) )
!= ( c_lessequals @ C @ ( c_Zorn_OTFin @ D @ E ) @ ( tc_set @ ( tc_set @ ( tc_set @ E ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,14]) ).
thf(24,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( c_Zorn_OTFin @ F @ I )),bind(B,$thf( tc_set @ ( tc_set @ I ) )),bind(C,$thf( c_Zorn_OTFin @ F @ I )),bind(D,$thf( F )),bind(E,$thf( I ))]]) ).
thf(25,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(1,negated_conjecture,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(7,plain,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( A
!= ( c_Zorn_Osucc @ B @ A @ C ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( A
!= ( c_Zorn_Osucc @ B @ A @ C ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( A
!= ( c_Zorn_Osucc @ B @ A @ C ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Zorn_Osucc @ B @ A @ C )
!= A )
| ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Zorn_Osucc @ B @ A @ C )
!= A )
| ~ ( c_in @ D @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( ( c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
!= ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,17]) ).
thf(35,plain,
! [A: $i] :
( ( ( c_Zorn_Osucc @ v_S @ v_m @ t_a )
!= v_m )
| ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( v_m )),bind(B,$thf( v_S )),bind(C,$thf( t_a ))]]) ).
thf(43,plain,
! [A: $i] :
( ( ( c_Zorn_Osucc @ v_S @ v_m @ t_a )
!= v_m )
| ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[35]) ).
thf(2,negated_conjecture,
( v_m
= ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,plain,
( v_m
= ( c_Zorn_Osucc @ v_S @ v_m @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ( c_Zorn_Osucc @ v_S @ v_m @ t_a )
= v_m ),
inference(lifteq,[status(thm)],[8]) ).
thf(77,plain,
! [A: $i] :
( ( v_m != v_m )
| ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(rewrite,[status(thm)],[43,10]) ).
thf(78,plain,
! [A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( c_lessequals @ A @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ C @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) )
!= ( c_in @ C @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,78]) ).
thf(85,plain,
c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( v_S )),bind(B,$thf( t_a )),bind(C,$thf( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ))]]) ).
thf(3,negated_conjecture,
~ ( c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,plain,
~ ( c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
~ ( c_lessequals @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(89,plain,
$false,
inference(rewrite,[status(thm)],[85,11]) ).
thf(90,plain,
$false,
inference(simp,[status(thm)],[89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SET844-2 : TPTP v8.2.0. Released v3.2.0.
% 0.05/0.13 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 12:54:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.84/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.02 % [INFO] Parsing done (110ms).
% 1.15/1.03 % [INFO] Running in sequential loop mode.
% 1.52/1.27 % [INFO] nitpick registered as external prover.
% 1.52/1.28 % [INFO] Scanning for conjecture ...
% 1.63/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.79/1.37 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.85/1.37 % [INFO] Problem is propositional (TPTP CNF).
% 1.85/1.38 % [INFO] Type checking passed.
% 1.85/1.38 % [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 ...
% 4.82/2.37 % [INFO] Killing All external provers ...
% 4.82/2.38 % Time passed: 1900ms (effective reasoning time: 1340ms)
% 4.82/2.38 % Axioms used in derivation (3): cls_Set_Osubset__refl_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_Oeq__succ__upper_0
% 4.82/2.38 % No. of inferences in proof: 29
% 4.82/2.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1900 ms resp. 1340 ms w/o parsing
% 4.82/2.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.82/2.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------