TSTP Solution File: SET858-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET858-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:54:41 EDT 2023
% Result : Unsatisfiable 2.81s 1.65s
% Output : Refutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 21
% Syntax : Number of formulae : 33 ( 11 unt; 10 typ; 0 def)
% Number of atoms : 67 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 500 ( 34 ~; 44 |; 0 &; 422 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% 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(v_n_type,type,
v_n: $i ).
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(c_Zorn_OTFin__linear__lemma1__1_type,type,
c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).
thf(9,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 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C )
!= A )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
thf(25,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 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C )
!= A )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(14,plain,
~ ( c_lessequals @ v_n @ v_m @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Zorn_Osucc @ B @ A @ C ) @ ( tc_set @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,plain,
c_in @ v_n @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
c_in @ v_m @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,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(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ A @ ( tc_set @ C ) )
| ( c_lessequals @ D @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ D @ A @ ( tc_set @ C ) )
| ( c_lessequals @ D @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,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 ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
thf(23,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 ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,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 ) ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
thf(30,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 ) ) )
| ~ ( c_lessequals @ A @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,negated_conjecture,
~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,plain,
~ ( c_lessequals @ v_m @ v_n @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,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 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ B @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
thf(28,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 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ B @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ C ) @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,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 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
thf(21,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 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ B @ A @ C ) @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ D @ A @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ B @ A @ C ) @ D @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[25,14,20,13,12,18,23,30,15,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET858-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 18:41:31 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.91/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.96 % [INFO] Parsing done (117ms).
% 1.22/0.96 % [INFO] Running in sequential loop mode.
% 1.68/1.16 % [INFO] eprover registered as external prover.
% 1.68/1.17 % [INFO] cvc4 registered as external prover.
% 1.68/1.17 % [INFO] Scanning for conjecture ...
% 1.68/1.23 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.87/1.25 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.87/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 2.02/1.28 % [INFO] Type checking passed.
% 2.02/1.28 % [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 ...
% 2.81/1.65 % External prover 'e' found a proof!
% 2.81/1.65 % [INFO] Killing All external provers ...
% 2.81/1.65 % Time passed: 1134ms (effective reasoning time: 683ms)
% 2.81/1.65 % 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)>
% 2.81/1.65 % Axioms used in derivation (7): cls_Zorn_OTFin__linear__lemma1_0, cls_Zorn_OTFin__linear__lemma1_3, cls_Set_Osubset__trans_0, cls_Zorn_OTFin__linear__lemma1_2, cls_Zorn_OAbrial__axiom1_0, cls_Zorn_OTFin__linear__lemma2_0, cls_Zorn_OTFin__linear__lemma1_1
% 2.81/1.65 % No. of inferences in proof: 23
% 2.81/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1134 ms resp. 683 ms w/o parsing
% 3.14/1.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.14/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------