%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM165^1 : TPTP v9.3.1. Released v7.0.0.
% 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 : n008.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 07:46:18 AM UTC 2026
% Result : Theorem 4.57s 1.84s
% Output : Refutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 14 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 88 ( 10 ~; 0 |; 10 &; 64 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(binDag_Mirabelle_dag_type,type,
binDag_Mirabelle_dag: $tType ).
thf(simpl_ref_type,type,
simpl_ref: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(binDag_Mirabelle_DAG_decl,type,
binDag_Mirabelle_DAG: binDag_Mirabelle_dag > $o ).
thf(binDag476092410e_Node_decl,type,
binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag ).
thf(binDag1380252983set_of_decl,type,
binDag1380252983set_of: binDag_Mirabelle_dag > ( set @ simpl_ref ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a_decl,type,
a: simpl_ref ).
thf(l_decl,type,
l: binDag_Mirabelle_dag ).
thf(r_decl,type,
r: binDag_Mirabelle_dag ).
thf(thesis_decl,type,
thesis: $o ).
thf(y_decl,type,
y: binDag_Mirabelle_dag ).
thf(4,axiom,
! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag,E: simpl_ref,F: binDag_Mirabelle_dag] :
( ( ( binDag476092410e_Node @ A @ B @ C )
= ( binDag476092410e_Node @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_dag_Oinject) ).
thf(10,plain,
! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag,E: simpl_ref,F: binDag_Mirabelle_dag] :
( ( ( binDag476092410e_Node @ A @ B @ C )
= ( binDag476092410e_Node @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
binDag_Mirabelle_DAG @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_DAG__y) ).
thf(9,plain,
binDag_Mirabelle_DAG @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( y
= ( binDag476092410e_Node @ l @ a @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Node) ).
thf(13,plain,
( y
= ( binDag476092410e_Node @ l @ a @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
( ~ ( member @ simpl_ref @ a @ ( binDag1380252983set_of @ l ) )
=> ( ~ ( member @ simpl_ref @ a @ ( binDag1380252983set_of @ r ) )
=> thesis ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(18,plain,
( ~ ( member @ simpl_ref @ a @ ( binDag1380252983set_of @ l ) )
=> ( ~ ( member @ simpl_ref @ a @ ( binDag1380252983set_of @ r ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
thesis,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ thesis,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_DAG @ ( binDag476092410e_Node @ A @ B @ C ) )
= ( ~ ( member @ simpl_ref @ B @ ( binDag1380252983set_of @ A ) )
& ~ ( member @ simpl_ref @ B @ ( binDag1380252983set_of @ C ) )
& ( binDag_Mirabelle_DAG @ A )
& ( binDag_Mirabelle_DAG @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_DAG_Osimps_I2_J) ).
thf(15,plain,
! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_DAG @ ( binDag476092410e_Node @ A @ B @ C ) )
= ( ~ ( member @ simpl_ref @ B @ ( binDag1380252983set_of @ A ) )
& ~ ( member @ simpl_ref @ B @ ( binDag1380252983set_of @ C ) )
& ( binDag_Mirabelle_DAG @ A )
& ( binDag_Mirabelle_DAG @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[10,9,13,18,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM165^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % 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
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:48:24 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.68/0.51 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.44/0.79 % [INFO] Parsing done (276ms).
% 1.44/0.79 % [INFO] Running in sequential loop mode.
% 2.75/1.08 % [INFO] eprover registered as external prover.
% 2.75/1.09 % [INFO] Scanning for conjecture ...
% 3.17/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 293 axioms. Running axiom selection ...
% 3.17/1.29 % [INFO] Axiom selection finished. Selected 5 axioms (removed 288 axioms).
% 3.40/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 3.40/1.32 % [INFO] Type checking passed.
% 3.40/1.32 % [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 ...
% 4.57/1.83 % External prover 'e' found a proof!
% 4.57/1.84 % [INFO] Killing All external provers ...
% 4.57/1.84 % Time passed: 1554ms (effective reasoning time: 1039ms)
% 4.57/1.84 % 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)>
% 4.57/1.84 % Axioms used in derivation (5): fact_1_dag_Oinject, fact_2_DAG_Osimps_I2_J, fact_12_DAG__y, fact_0_Node, conj_0
% 4.57/1.84 % No. of inferences in proof: 14
% 4.57/1.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1554 ms resp. 1039 ms w/o parsing
% 4.57/1.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.57/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------