TSTP Solution File: PUZ062-2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : PUZ062-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 02:26:46 EDT 2024
% Result : Unsatisfiable 3.26s 1.72s
% Output : Refutation 3.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 34
% Syntax : Number of formulae : 48 ( 17 unt; 21 typ; 0 def)
% Number of atoms : 41 ( 12 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 386 ( 16 ~; 14 |; 0 &; 356 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 12 con; 0-4 aty)
% Number of variables : 40 ( 0 ^ 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_t_type,type,
v_t: $i ).
thf(c_Mutil_Otiling_type,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(c_Mutil_Odomino_type,type,
c_Mutil_Odomino: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_inter_type,type,
c_inter: $i > $i > $i > $i ).
thf(c_Mutil_Ocoloured_type,type,
c_Mutil_Ocoloured: $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(v_a_type,type,
v_a: $i ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(c_insert_type,type,
c_insert: $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_i_type,type,
v_i: $i ).
thf(v_j_type,type,
v_j: $i ).
thf(v_m_type,type,
v_m: $i ).
thf(v_n_type,type,
v_n: $i ).
thf(c_Finite__Set_OFinites_type,type,
c_Finite__Set_OFinites: $i ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_insert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,negated_conjecture,
( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(14,plain,
( ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ ( c_inter @ C @ A @ B ) @ c_Finite__Set_OFinites @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,negated_conjecture,
( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(17,plain,
( ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_Finite__Set_Ocard @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( c_in @ A @ ( c_inter @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(18,plain,
( ( c_inter @ v_a @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ C @ A @ B )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ B ) )
| ( c_in @ C @ A @ B )
| ( ( c_Finite__Set_Ocard @ ( c_insert @ C @ A @ B ) @ B )
= ( c_Suc @ ( c_Finite__Set_Ocard @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,negated_conjecture,
( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(19,plain,
( ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_a @ ( tc_prod @ tc_nat @ tc_nat ) )
= ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ c_emptyset @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
c_in @ v_t @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(38,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ c_emptyset @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ ( c_inter @ B @ C @ D ) @ D )
| ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(16,plain,
( ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_i @ v_j @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ c_0 ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) )
!= ( c_Finite__Set_Ocard @ ( c_insert @ ( c_Pair @ v_m @ v_n @ tc_nat @ tc_nat ) @ ( c_inter @ ( c_Mutil_Ocoloured @ ( c_Suc @ c_0 ) ) @ v_t @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_prod @ tc_nat @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( c_in @ A @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
thf(31,plain,
! [A: $i] :
( ~ ( c_in @ A @ ( c_Mutil_Otiling @ c_Mutil_Odomino @ ( tc_prod @ tc_nat @ tc_nat ) ) @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) )
| ( c_in @ A @ c_Finite__Set_OFinites @ ( tc_set @ ( tc_prod @ tc_nat @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[37,14,29,17,35,18,26,19,15,38,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : PUZ062-2 : TPTP v8.2.0. Released v3.2.0.
% 0.16/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n002.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sat May 18 10:42:39 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (106ms).
% 1.34/0.98 % [INFO] Running in sequential loop mode.
% 1.72/1.18 % [INFO] eprover registered as external prover.
% 1.72/1.18 % [INFO] cvc4 registered as external prover.
% 1.72/1.18 % [INFO] Scanning for conjecture ...
% 1.87/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.93/1.27 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.93/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.93/1.29 % [INFO] Type checking passed.
% 1.93/1.29 % [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 ...
% 3.26/1.72 % External prover 'e' found a proof!
% 3.26/1.72 % [INFO] Killing All external provers ...
% 3.26/1.72 % Time passed: 1189ms (effective reasoning time: 734ms)
% 3.26/1.72 % Axioms used in derivation (7): cls_Set_OInt__iff_2, cls_Finite__Set_Ocard__insert__disjoint_0, cls_Set_Oinsert__iff_1, cls_Mutil_Otiling__domino__finite_0, cls_Set_OInt__iff_1, cls_Finite__Set_Ofinite__Int_1, cls_Set_Oempty__iff_0
% 3.26/1.72 % No. of inferences in proof: 27
% 3.26/1.72 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1189 ms resp. 734 ms w/o parsing
% 3.26/1.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.26/1.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------