%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n007.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 : Wed Sep 30 08:06:37 AM UTC 2026
% Result : Theorem 5.13s 2.97s
% Output : Refutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 32 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 12 ~; 4 |; 8 &; 125 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 2 ^; 78 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(tree_b_type,type,
tree_b: $tType ).
thf(b_type,type,
b: $tType ).
thf(heapIm229596387mpty_b_decl,type,
heapIm229596387mpty_b: tree_b > $o ).
thf(heapIm1140443834left_b_decl,type,
heapIm1140443834left_b: tree_b > tree_b ).
thf(heapIm1257206335ight_b_decl,type,
heapIm1257206335ight_b: tree_b > tree_b ).
thf(e_b_decl,type,
e_b: tree_b ).
thf(t_b_decl,type,
t_b: b > tree_b > tree_b > tree_b ).
thf(pred_Tree_b_decl,type,
pred_Tree_b: ( b > $o ) > tree_b > $o ).
thf(in_tree_b_decl,type,
in_tree_b: b > tree_b > $o ).
thf(val_b_decl,type,
val_b: tree_b > b ).
thf(ord_less_eq_Tree_b_o_decl,type,
ord_less_eq_Tree_b_o: ( tree_b > $o ) > ( tree_b > $o ) > $o ).
thf(ord_less_eq_b_o_decl,type,
ord_less_eq_b_o: ( b > $o ) > ( b > $o ) > $o ).
thf(12,axiom,
! [A: b,B: tree_b,C: tree_b] :
( ( heapIm1140443834left_b @ ( t_b @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_left_Osimps) ).
thf(56,plain,
! [A: b,B: tree_b,C: tree_b] :
( ( heapIm1140443834left_b @ ( t_b @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [A: b,B: tree_b,C: tree_b] :
( e_b
!= ( t_b @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Tree_Odistinct_I1_J) ).
thf(52,plain,
! [A: b,B: tree_b,C: tree_b] :
( e_b
!= ( t_b @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: tree_b] :
( ( A != e_b )
=> ~ ! [B: b,C: tree_b,D: tree_b] :
( A
!= ( t_b @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_Tree_Oexhaust) ).
thf(33,plain,
! [A: tree_b] :
( ( A != e_b )
=> ~ ! [B: b,C: tree_b,D: tree_b] :
( A
!= ( t_b @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
heapIm229596387mpty_b @ e_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( heapIm229596387mpty_b @ e_b ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ( heapIm229596387mpty_b @ e_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: b > $o,B: b > $o] :
( ( ord_less_eq_b_o @ A @ B )
=> ( ord_less_eq_Tree_b_o @ ( pred_Tree_b @ A ) @ ( pred_Tree_b @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Tree_Opred__mono) ).
thf(62,plain,
! [A: b > $o,B: b > $o] :
( ( ord_less_eq_b_o @ A @ B )
=> ( ord_less_eq_Tree_b_o @ ( pred_Tree_b @ A ) @ ( pred_Tree_b @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: b,B: tree_b,C: tree_b,D: b,E: tree_b,F: tree_b] :
( ( ( t_b @ A @ B @ C )
= ( t_b @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_Tree_Oinject) ).
thf(24,plain,
! [A: b,B: tree_b,C: tree_b,D: b,E: tree_b,F: tree_b] :
( ( ( t_b @ A @ B @ C )
= ( t_b @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: tree_b > $o,B: tree_b] :
( ( A @ e_b )
=> ( ! [C: b,D: tree_b,E: tree_b] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t_b @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Tree_Oinduct) ).
thf(37,plain,
! [A: tree_b > $o,B: tree_b] :
( ( A @ e_b )
=> ( ! [C: b,D: tree_b,E: tree_b] :
( ( A @ D )
=> ( ( A @ E )
=> ( A @ ( t_b @ C @ D @ E ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: b,B: tree_b,C: tree_b] :
( ( val_b @ ( t_b @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_val_Osimps) ).
thf(64,plain,
! [A: b,B: tree_b,C: tree_b] :
( ( val_b @ ( t_b @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
( heapIm229596387mpty_b
= ( ^ [A: tree_b] : ( A = e_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_hs__is__empty__def) ).
thf(17,plain,
( heapIm229596387mpty_b
= ( ^ [A: tree_b] : ( A = e_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: b > $o] : ( pred_Tree_b @ A @ e_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Tree_Opred__inject_I1_J) ).
thf(22,plain,
! [A: b > $o] : ( pred_Tree_b @ A @ e_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
! [A: b,B: tree_b,C: tree_b] :
( ( heapIm1257206335ight_b @ ( t_b @ A @ B @ C ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_right_Osimps) ).
thf(59,plain,
! [A: b,B: tree_b,C: tree_b] :
( ( heapIm1257206335ight_b @ ( t_b @ A @ B @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: b > $o,B: b,C: tree_b,D: tree_b] :
( ( pred_Tree_b @ A @ ( t_b @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree_b @ A @ C )
& ( pred_Tree_b @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_Tree_Opred__inject_I2_J) ).
thf(27,plain,
! [A: b > $o,B: b,C: tree_b,D: tree_b] :
( ( pred_Tree_b @ A @ ( t_b @ B @ C @ D ) )
= ( ( A @ B )
& ( pred_Tree_b @ A @ C )
& ( pred_Tree_b @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: b,B: b,C: tree_b,D: tree_b] :
( ( in_tree_b @ A @ ( t_b @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree_b @ A @ C )
| ( in_tree_b @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__tree_Osimps_I2_J) ).
thf(30,plain,
! [A: b,B: b,C: tree_b,D: tree_b] :
( ( in_tree_b @ A @ ( t_b @ B @ C @ D ) )
= ( ( A = B )
| ( in_tree_b @ A @ C )
| ( in_tree_b @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: b] :
~ ( in_tree_b @ A @ e_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_in__tree_Osimps_I1_J) ).
thf(19,plain,
! [A: b] :
~ ( in_tree_b @ A @ e_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(67,plain,
$false,
inference(e,[status(thm)],[56,52,33,16,62,24,37,64,17,22,59,27,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP065^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.07 % 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
% 0.09/0.21 % Computer : n007.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:43:41 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.19/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.14 % [INFO] Parsing done (232ms).
% 1.72/1.16 % [INFO] Running in sequential loop mode.
% 2.47/1.62 % [INFO] eprover registered as external prover.
% 2.47/1.63 % [INFO] Scanning for conjecture ...
% 2.68/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.68/1.75 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.85/1.84 % [INFO] Problem is higher-order (TPTP THF).
% 2.85/1.85 % [INFO] Type checking passed.
% 2.85/1.86 % [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 ...
% 5.13/2.96 % External prover 'e' found a proof!
% 5.13/2.96 % [INFO] Killing All external provers ...
% 5.13/2.96 % Time passed: 2586ms (effective reasoning time: 1788ms)
% 5.13/2.96 % 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)>
% 5.13/2.97 % Axioms used in derivation (13): fact_10_right_Osimps, fact_4_Tree_Opred__inject_I2_J, fact_9_left_Osimps, fact_12_val_Osimps, fact_7_Tree_Oinduct, fact_2_Tree_Opred__inject_I1_J, fact_1_in__tree_Osimps_I1_J, fact_3_Tree_Oinject, fact_0_hs__is__empty__def, fact_8_Tree_Odistinct_I1_J, fact_11_Tree_Opred__mono, fact_6_Tree_Oexhaust, fact_5_in__tree_Osimps_I2_J
% 5.13/2.97 % No. of inferences in proof: 30
% 5.13/2.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2586 ms resp. 1788 ms w/o parsing
% 5.50/3.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.50/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------