TSTP Solution File: SET849-2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET849-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 03:07:10 EDT 2024
% Result : Unsatisfiable 2.56s 1.61s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 28 ( 11 unt; 8 typ; 0 def)
% Number of atoms : 31 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 319 ( 14 ~; 9 |; 0 &; 296 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 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 : 34 ( 0 ^ 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
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_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(1,negated_conjecture,
( ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(5,plain,
( ( 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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,plain,
( ( 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 ) ) ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( 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 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(4,axiom,
! [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 ) ) )
| ( ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) )
= ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).
thf(11,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 ) ) )
| ( ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) )
= ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,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 ) ) )
| ( ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) )
= ( c_Zorn_Osucc @ A @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ B ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( ( 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 ) ) )
| ~ ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(2,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(8,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,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(9,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)],[3]) ).
thf(10,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)],[9]) ).
thf(14,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)],[8,10]) ).
thf(15,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Union @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ B ) ) @ ( c_Zorn_OTFin @ A @ B ) @ ( tc_set @ ( tc_set @ B ) ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$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(16,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)],[15]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( 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 ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[13,16]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( 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 ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
( ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) )
!= ( c_Union @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ t_a ) ) ),
inference(rewrite,[status(thm)],[7,18]) ).
thf(20,plain,
$false,
inference(simp,[status(thm)],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET849-2 : TPTP v8.2.0. Released v3.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n020.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 : Mon May 20 12:25:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.00/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.97 % [INFO] Parsing done (103ms).
% 1.13/0.98 % [INFO] Running in sequential loop mode.
% 1.44/1.18 % [INFO] nitpick registered as external prover.
% 1.66/1.18 % [INFO] Scanning for conjecture ...
% 1.73/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.81/1.25 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.81/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.81/1.26 % [INFO] Type checking passed.
% 1.81/1.27 % [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 ...
% 2.56/1.57 % [INFO] Killing All external provers ...
% 2.56/1.61 % Time passed: 1074ms (effective reasoning time: 622ms)
% 2.56/1.61 % Axioms used in derivation (3): cls_Zorn_Oequal__succ__Union_1, cls_Set_Osubset__refl_0, cls_Zorn_OTFin__UnionI_0
% 2.56/1.61 % No. of inferences in proof: 20
% 2.56/1.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1074 ms resp. 622 ms w/o parsing
% 2.85/1.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.85/1.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------