TSTP Solution File: LAT281-2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : LAT281-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Mon May 20 23:30:41 EDT 2024
% Result : Unsatisfiable 4.76s 2.45s
% Output : Refutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 44 ( 17 unt; 14 typ; 0 def)
% Number of atoms : 60 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 430 ( 35 ~; 24 |; 0 &; 371 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 33 ( 0 ^ 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_a_type,type,
v_a: $i ).
thf(v_b_type,type,
v_b: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_r_type,type,
v_r: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(v_c_type,type,
v_c: $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Tarski_OPartialOrder_type,type,
c_Tarski_OPartialOrder: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_type,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(tc_Product__Type_Ounit_type,type,
tc_Product__Type_Ounit: $i ).
thf(c_Tarski_Opotype_Oorder_type,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(v_cl_type,type,
v_cl: $i ).
thf(2,negated_conjecture,
c_in @ ( c_Pair @ v_b @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,plain,
c_in @ ( c_Pair @ v_b @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Otrans__def_0) ).
thf(12,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(3,negated_conjecture,
~ ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(10,plain,
~ ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
~ ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ ( c_Pair @ E @ C @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
| ( ( c_in @ ( c_Pair @ E @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) )
!= ( c_in @ ( c_Pair @ v_a @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(52,plain,
! [A: $i] :
( ~ ( c_Relation_Otrans @ v_r @ t_a )
| ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( v_r )),bind(B,$thf( t_a )),bind(C,$thf( C )),bind(D,$thf( v_c )),bind(E,$thf( v_a ))]]) ).
thf(70,plain,
! [A: $i] :
( ~ ( c_Relation_Otrans @ v_r @ t_a )
| ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(6,axiom,
c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
thf(16,plain,
c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) )
| ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ A @ B @ tc_Product__Type_Ounit ) @ B )
| ( ( c_in @ v_cl @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ t_a @ tc_Product__Type_Ounit ) )
!= ( c_in @ A @ c_Tarski_OPartialOrder @ ( tc_Tarski_Opotype_Opotype__ext__type @ B @ tc_Product__Type_Ounit ) ) ) ),
inference(paramod_ordered,[status(thm)],[16,15]) ).
thf(33,plain,
c_Relation_Otrans @ ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) @ t_a,
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( v_cl )),bind(B,$thf( t_a ))]]) ).
thf(7,axiom,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(17,plain,
( v_r
= ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
( ( c_Tarski_Opotype_Oorder @ v_cl @ t_a @ tc_Product__Type_Ounit )
= v_r ),
inference(lifteq,[status(thm)],[17]) ).
thf(77,plain,
c_Relation_Otrans @ v_r @ t_a,
inference(rewrite,[status(thm)],[33,18]) ).
thf(83,plain,
! [A: $i] :
( ~ $true
| ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(rewrite,[status(thm)],[70,77]) ).
thf(84,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
! [A: $i] :
( ~ ( c_in @ ( c_Pair @ v_a @ A @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
| ( ( c_in @ ( c_Pair @ v_b @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) )
!= ( c_in @ ( c_Pair @ A @ v_c @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,84]) ).
thf(86,plain,
~ ( c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( v_b ))]]) ).
thf(1,negated_conjecture,
c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(8,plain,
c_in @ ( c_Pair @ v_a @ v_b @ t_a @ t_a ) @ v_r @ ( tc_prod @ t_a @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(109,plain,
~ $true,
inference(rewrite,[status(thm)],[86,8]) ).
thf(110,plain,
$false,
inference(simp,[status(thm)],[109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT281-2 : TPTP v8.2.0. Released v3.2.0.
% 0.10/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun May 19 19:54:54 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.93/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.05 % [INFO] Parsing done (155ms).
% 1.18/1.07 % [INFO] Running in sequential loop mode.
% 1.74/1.42 % [INFO] nitpick registered as external prover.
% 1.74/1.42 % [INFO] Scanning for conjecture ...
% 1.94/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.99/1.54 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.99/1.56 % [INFO] Problem is propositional (TPTP CNF).
% 1.99/1.56 % [INFO] Type checking passed.
% 1.99/1.56 % [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 ...
% 4.76/2.44 % [INFO] Killing All external provers ...
% 4.76/2.45 % Time passed: 1994ms (effective reasoning time: 1372ms)
% 4.76/2.45 % Axioms used in derivation (4): cls_Relation_Otrans__def_0, cls_Tarski_Ocl_A_58_APartialOrder_0, cls_Tarski_OPartialOrder__iff_2, cls_Tarski_Or_A_61_61_Aorder_Acl_0
% 4.76/2.45 % No. of inferences in proof: 30
% 4.76/2.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1994 ms resp. 1372 ms w/o parsing
% 4.76/2.50 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.76/2.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------