TSTP Solution File: SET847-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:54:36 EDT 2023
% Result : Unsatisfiable 2.86s 1.64s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 24
% Syntax : Number of formulae : 36 ( 9 unt; 13 typ; 0 def)
% Number of atoms : 41 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 286 ( 20 ~; 18 |; 0 &; 248 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Zorn_Omaxchain_type,type,
c_Zorn_Omaxchain: $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_minus_type,type,
c_minus: $i > $i > $i > $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Main_OsubsetI__1_type,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_OTFin_type,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(c_Union_type,type,
c_Union: $i > $i > $i ).
thf(c_Zorn_Ochain_type,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(c_Zorn_Osucc_type,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_minus @ B @ D @ ( tc_set @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oequal__succ__Union_1) ).
thf(29,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)],[10]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ ( c_Zorn_Ochain @ B @ C ) @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( ( c_Zorn_Osucc @ B @ A @ C )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_minus @ ( c_Zorn_Ochain @ B @ C ) @ ( c_Zorn_Omaxchain @ B @ C ) @ ( tc_set @ ( tc_set @ ( tc_set @ C ) ) ) ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( ( c_Zorn_Osucc @ B @ A @ C )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ A @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_Zorn_OTFin @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) )
| ( c_in @ A @ ( c_Zorn_Ochain @ B @ C ) @ ( tc_set @ ( tc_set @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( c_in @ A @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
! [A: $i] :
~ ( c_in @ A @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(18,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
thf(16,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ A @ B @ C ) @ A @ C )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,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(24,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,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(25,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)],[8]) ).
thf(35,plain,
$false,
inference(e,[status(thm)],[14,29,21,32,27,12,18,16,19,24,25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET847-2 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % 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 : Thu May 18 19:06:44 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.96 % [INFO] Parsing done (118ms).
% 1.19/0.97 % [INFO] Running in sequential loop mode.
% 1.51/1.18 % [INFO] eprover registered as external prover.
% 1.74/1.18 % [INFO] cvc4 registered as external prover.
% 1.74/1.19 % [INFO] Scanning for conjecture ...
% 1.87/1.24 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.87/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.28 % [INFO] Type checking passed.
% 1.87/1.29 % [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 ...
% 2.86/1.63 % External prover 'e' found a proof!
% 2.86/1.63 % [INFO] Killing All external provers ...
% 2.86/1.64 % Time passed: 1119ms (effective reasoning time: 663ms)
% 2.86/1.64 % 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)>
% 2.86/1.64 % Axioms used in derivation (10): cls_Set_OemptyE_0, cls_Set_Osubset__refl_0, cls_Set_OsubsetI_0, cls_Zorn_Osucc__not__equals_0, cls_Set_Oempty__subsetI_0, cls_Set_Osubset__antisym_0, cls_Zorn_Oequal__succ__Union_1, cls_Set_ODiffI_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_OTFin__chain__lemma4_0
% 2.86/1.64 % No. of inferences in proof: 23
% 2.86/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1119 ms resp. 663 ms w/o parsing
% 2.86/1.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.86/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------