%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 08:21:16 AM UTC 2026
% Result : Unsatisfiable 5.32s 8.40s
% Output : Refutation 5.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 17 unt; 0 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 : 0 ( 0 >; 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_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_t_decl,type,
v_t: $i ).
thf(c_Mutil_Otiling_decl,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(c_Mutil_Odomino_decl,type,
c_Mutil_Odomino: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_Mutil_Ocoloured_decl,type,
c_Mutil_Ocoloured: $i > $i ).
thf(c_0_decl,type,
c_0: $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_i_decl,type,
v_i: $i ).
thf(v_j_decl,type,
v_j: $i ).
thf(v_m_decl,type,
v_m: $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,negated_conjecture,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_a @ ( c_0 @ c_Suc @ c_Mutil_Ocoloured @ c_inter ) ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_Pair ) ) ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(14,plain,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_a @ ( c_0 @ c_Suc @ c_Mutil_Ocoloured @ c_inter ) ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_Pair ) ) ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,negated_conjecture,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Mutil_Ocoloured @ c_inter ) ) @ c_Finite__Set_Ocard ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Suc @ c_Mutil_Ocoloured @ c_inter ) ) @ c_Finite__Set_Ocard ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(17,plain,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Mutil_Ocoloured @ c_inter ) ) @ c_Finite__Set_Ocard ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Suc @ c_Mutil_Ocoloured @ c_inter ) ) @ c_Finite__Set_Ocard ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(35,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,negated_conjecture,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( v_a @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(18,plain,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( v_a @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ ( C @ c_insert ) ) @ c_Finite__Set_Ocard ) )
= ( B @ ( A @ c_Finite__Set_Ocard ) @ c_Suc ) )
| ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ ( C @ c_insert ) ) @ c_Finite__Set_Ocard ) )
= ( B @ ( A @ c_Finite__Set_Ocard ) @ c_Suc ) )
| ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,negated_conjecture,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_a @ ( c_0 @ c_Mutil_Ocoloured @ c_inter ) ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( v_j @ ( v_i @ c_Pair ) ) ) @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(19,plain,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_a @ ( c_0 @ c_Mutil_Ocoloured @ c_inter ) ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( v_j @ ( v_i @ c_Pair ) ) ) @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,negated_conjecture,
tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Mutil_Odomino @ c_Mutil_Otiling ) @ ( v_t @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Mutil_Odomino @ c_Mutil_Otiling ) @ ( v_t @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(38,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Mutil_Ocoloured @ c_inter ) ) @ ( tc_nat @ ( tc_nat @ ( v_j @ ( v_i @ c_Pair ) ) ) @ c_insert ) ) @ c_Finite__Set_Ocard ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Suc @ c_Mutil_Ocoloured @ c_inter ) ) @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_Pair ) ) ) @ c_insert ) ) @ c_Finite__Set_Ocard ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(16,plain,
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Mutil_Ocoloured @ c_inter ) ) @ ( tc_nat @ ( tc_nat @ ( v_j @ ( v_i @ c_Pair ) ) ) @ c_insert ) ) @ c_Finite__Set_Ocard ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( v_t @ ( c_0 @ c_Suc @ c_Mutil_Ocoloured @ c_inter ) ) @ ( tc_nat @ ( tc_nat @ ( v_n @ ( v_m @ c_Pair ) ) ) @ c_insert ) ) @ c_Finite__Set_Ocard ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Mutil_Odomino @ c_Mutil_Otiling ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
thf(31,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Mutil_Odomino @ c_Mutil_Otiling ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,plain,
$false,
inference(e,[status(thm)],[37,14,29,17,35,18,26,19,15,38,33,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : PUZ062-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/5.71 % Computer : n018.cluster.edu
% 0.24/5.71 % Model : x86_64 x86_64
% 0.24/5.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.71 % Memory : 8046.5625MB
% 0.24/5.71 % OS : Linux 6.8.0-71-generic
% 0.24/5.71 % CPULimit : 300
% 0.24/5.71 % WCLimit : 300
% 0.24/5.71 % DateTime : Sat Sep 26 05:12:57 UTC 2026
% 0.24/5.71 % CPUTime :
% 0.24/5.71 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.14/6.39 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/6.67 % [INFO] Parsing done (270ms).
% 1.67/6.69 % [INFO] Running in sequential loop mode.
% 2.72/7.28 % [INFO] eprover registered as external prover.
% 2.72/7.29 % [INFO] Scanning for conjecture ...
% 3.12/7.46 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.30/7.51 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.30/7.52 % [INFO] Problem is propositional (TPTP CNF).
% 3.30/7.53 % [INFO] Type checking passed.
% 3.30/7.54 % [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 ...
% 5.32/8.39 % External prover 'e' found a proof!
% 5.32/8.39 % [INFO] Killing All external provers ...
% 5.32/8.39 % Time passed: 2476ms (effective reasoning time: 1695ms)
% 5.32/8.39 % 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
% 5.32/8.39 % No. of inferences in proof: 27
% 5.32/8.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2476 ms resp. 1695 ms w/o parsing
% 5.70/8.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.70/8.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------