TSTP Solution File: SET846-2 by Leo-III-SAT---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET846-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 7 10:50:41 EDT 2024
% Result : Unsatisfiable 4.05s 1.83s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 33 ( 13 unt; 8 typ; 0 def)
% Number of atoms : 43 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 391 ( 16 ~; 12 |; 0 &; 363 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 0 ^ 58 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(v_S_type,type,
v_S: $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(1,negated_conjecture,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(6,plain,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,plain,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ t_a ) @ ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(10,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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/sandbox/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(20,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)],[10,14]) ).
thf(21,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$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(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(simp,[status(thm)],[21]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(30,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Zorn_Osucc @ D @ C @ E ) @ ( c_Zorn_OTFin @ D @ E ) @ ( tc_set @ ( tc_set @ E ) ) )
| ( ( 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 @ D @ E ) @ ( tc_set @ ( tc_set @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,12]) ).
thf(31,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( c_Union @ ( c_Zorn_OTFin @ H @ J ) @ ( tc_set @ J ) )),bind(D,$thf( H )),bind(E,$thf( J ))]]) ).
thf(41,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_Union @ B @ C ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_Union @ B @ C ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ ( c_Union @ B @ C ) @ ( tc_set @ C ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ C @ ( c_Union @ D @ E ) @ ( tc_set @ E ) )
| ( ( c_in @ ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) )
!= ( c_in @ C @ D @ ( tc_set @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,9]) ).
thf(55,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( N )),bind(B,$thf( P )),bind(C,$thf( c_Zorn_Osucc @ N @ ( c_Union @ ( c_Zorn_OTFin @ N @ P ) @ ( tc_set @ P ) ) @ P )),bind(D,$thf( c_Zorn_OTFin @ N @ P )),bind(E,$thf( tc_set @ P ))]]) ).
thf(58,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(60,plain,
~ $true,
inference(rewrite,[status(thm)],[7,58]) ).
thf(61,plain,
$false,
inference(simp,[status(thm)],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SET846-2 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 6 20:49:09 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.84/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/0.93 % [INFO] Parsing done (102ms).
% 1.02/0.93 % [INFO] Running in sequential loop mode.
% 1.46/1.12 % [INFO] nitpick registered as external prover.
% 1.46/1.13 % [INFO] Scanning for conjecture ...
% 1.65/1.18 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.75/1.19 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.75/1.20 % [INFO] Problem is propositional (TPTP CNF).
% 1.75/1.20 % [INFO] Type checking passed.
% 1.75/1.21 % [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 ...
% 4.05/1.82 % [INFO] Killing All external provers ...
% 4.05/1.82 % Time passed: 1320ms (effective reasoning time: 886ms)
% 4.05/1.82 % 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)>
% 4.05/1.83 % Axioms used in derivation (4): cls_Set_Osubset__refl_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_OTFin_OsuccI_0, cls_Set_OUnion__upper_0
% 4.05/1.83 % No. of inferences in proof: 25
% 4.05/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1320 ms resp. 886 ms w/o parsing
% 4.05/1.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.05/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------