%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT277-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:46:56 AM UTC 2026
% Result : Unsatisfiable 3.01s 2.33s
% Output : Refutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 118 ( 8 ~; 6 |; 0 &; 104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 12 ( 0 ^; 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Relation_Orefl_decl,type,
c_Relation_Orefl: $i > $i > $i > $o ).
thf(c_Tarski_Opotype_Opset_decl,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(v_cl_decl,type,
v_cl: $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Tarski_OPartialOrder_decl,type,
c_Tarski_OPartialOrder: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_decl,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(c_Tarski_Opotype_Oorder_decl,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(2,negated_conjecture,
~ ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_x @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,plain,
~ ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_x @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(13,plain,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
thf(17,plain,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(18,plain,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_Relation_Orefl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OreflD_0) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_Relation_Orefl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
t_a @ ( v_A @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(8,plain,
t_a @ ( v_A @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[9,13,17,18,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT277-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.51 % Computer : n014.cluster.edu
% 0.13/0.51 % Model : x86_64 x86_64
% 0.13/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.51 % Memory : 8046.5625MB
% 0.13/0.51 % OS : Linux 6.8.0-71-generic
% 0.13/0.51 % CPULimit : 300
% 0.13/0.51 % WCLimit : 300
% 0.13/0.51 % DateTime : Fri Sep 25 20:23:33 UTC 2026
% 0.13/0.51 % CPUTime :
% 0.13/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/1.08 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/1.26 % [INFO] Parsing done (177ms).
% 1.15/1.27 % [INFO] Running in sequential loop mode.
% 1.69/1.67 % [INFO] eprover registered as external prover.
% 1.69/1.68 % [INFO] Scanning for conjecture ...
% 1.88/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.03/1.81 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.03/1.82 % [INFO] Problem is propositional (TPTP CNF).
% 2.03/1.83 % [INFO] Type checking passed.
% 2.03/1.83 % [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 ...
% 3.01/2.33 % External prover 'e' found a proof!
% 3.01/2.33 % [INFO] Killing All external provers ...
% 3.01/2.33 % Time passed: 1689ms (effective reasoning time: 1047ms)
% 3.01/2.33 % Axioms used in derivation (5): cls_Tarski_OPartialOrder__iff_0, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Relation_OreflD_0, cls_Tarski_Ocl_A_58_APartialOrder_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0
% 3.01/2.33 % No. of inferences in proof: 15
% 3.01/2.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1689 ms resp. 1047 ms w/o parsing
% 3.01/2.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.01/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------