%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM170^1 : 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 : n026.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 6.49s 2.80s
% Output : Refutation 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 18
% Syntax : Number of formulae : 38 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 40 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 362 ( 12 ~; 6 |; 18 &; 300 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 130 ( 0 ^; 122 !; 8 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(binDag_Mirabelle_dag_type,type,
binDag_Mirabelle_dag: $tType ).
thf(simpl_ref_type,type,
simpl_ref: $tType ).
thf(binDag_Mirabelle_Dag_decl,type,
binDag_Mirabelle_Dag: simpl_ref > ( simpl_ref > simpl_ref ) > ( simpl_ref > simpl_ref ) > binDag_Mirabelle_dag > $o ).
thf(binDag476092410e_Node_decl,type,
binDag476092410e_Node: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > binDag_Mirabelle_dag ).
thf(binDag1297733282se_dag_decl,type,
binDag1297733282se_dag:
!>[TA: $tType] : ( TA > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA ) > binDag_Mirabelle_dag > TA ) ).
thf(binDag1442713106ec_dag_decl,type,
binDag1442713106ec_dag:
!>[TA: $tType] : ( TA > ( binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA ) > binDag_Mirabelle_dag > TA ) ).
thf(binDag786255756subdag_decl,type,
binDag786255756subdag: binDag_Mirabelle_dag > binDag_Mirabelle_dag > $o ).
thf(simpl_Null_decl,type,
simpl_Null: simpl_ref ).
thf(l_decl,type,
l: simpl_ref > simpl_ref ).
thf(lt_decl,type,
lt: binDag_Mirabelle_dag ).
thf(p_decl,type,
p: simpl_ref ).
thf(r_decl,type,
r: simpl_ref > simpl_ref ).
thf(rt_decl,type,
rt: binDag_Mirabelle_dag ).
thf(t_decl,type,
t: binDag_Mirabelle_dag ).
thf(thesis_decl,type,
thesis: $o ).
thf(15,axiom,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag,E: simpl_ref,F: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ ( binDag476092410e_Node @ D @ E @ F ) )
= ( ( A = E )
& ( A != simpl_Null )
& ( binDag_Mirabelle_Dag @ ( B @ A ) @ B @ C @ D )
& ( binDag_Mirabelle_Dag @ ( C @ A ) @ B @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Dag_Osimps_I2_J) ).
thf(61,plain,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag,E: simpl_ref,F: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ ( binDag476092410e_Node @ D @ E @ F ) )
= ( ( A = E )
& ( A != simpl_Null )
& ( binDag_Mirabelle_Dag @ ( B @ A ) @ B @ C @ D )
& ( binDag_Mirabelle_Dag @ ( C @ A ) @ B @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(17,axiom,
! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
( ( binDag1442713106ec_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
= ( B @ C @ D @ E @ ( binDag1442713106ec_dag @ TA @ A @ B @ C ) @ ( binDag1442713106ec_dag @ TA @ A @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_dag_Osimps_I7_J) ).
thf(65,plain,
! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA > TA > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
( ( binDag1442713106ec_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
= ( B @ C @ D @ E @ ( binDag1442713106ec_dag @ TA @ A @ B @ C ) @ ( binDag1442713106ec_dag @ TA @ A @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
=> ? [E: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ E )
& ! [F: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ F )
=> ( F = E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_Dag__unique1) ).
thf(41,plain,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
=> ? [E: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ E )
& ! [F: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ F )
=> ( F = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,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_3_dag_Oinject) ).
thf(54,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)],[13]) ).
thf(7,axiom,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ B )
=> ~ ( binDag786255756subdag @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_subdag__not__sym) ).
thf(35,plain,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ B )
=> ~ ( binDag786255756subdag @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
( t
!= ( binDag476092410e_Node @ A @ p @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_calculation) ).
thf(50,plain,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
( t
!= ( binDag476092410e_Node @ A @ p @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: simpl_ref] :
( ( binDag_Mirabelle_Dag @ A @ l @ r @ ( binDag476092410e_Node @ lt @ p @ rt ) )
=> thesis ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(72,plain,
! [A: simpl_ref] :
( ( binDag_Mirabelle_Dag @ A @ l @ r @ ( binDag476092410e_Node @ lt @ p @ rt ) )
=> thesis ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
binDag_Mirabelle_Dag @ ( r @ p ) @ l @ r @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(40,plain,
binDag_Mirabelle_Dag @ ( r @ p ) @ l @ r @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,axiom,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ B )
=> ( ( binDag786255756subdag @ B @ C )
=> ( binDag786255756subdag @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_subdag__trans) ).
thf(37,plain,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ B )
=> ( ( binDag786255756subdag @ B @ C )
=> ( binDag786255756subdag @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ ( binDag476092410e_Node @ A @ B @ C ) @ D )
= ( ( D = A )
| ( D = C )
| ( binDag786255756subdag @ A @ D )
| ( binDag786255756subdag @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_subdag_Osimps_I2_J) ).
thf(25,plain,
! [A: binDag_Mirabelle_dag,B: simpl_ref,C: binDag_Mirabelle_dag,D: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ ( binDag476092410e_Node @ A @ B @ C ) @ D )
= ( ( D = A )
| ( D = C )
| ( binDag786255756subdag @ A @ D )
| ( binDag786255756subdag @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(20,plain,
~ thesis,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag,E: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
=> ( ( binDag_Mirabelle_Dag @ A @ B @ C @ E )
=> ( D = E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Dag__unique) ).
thf(57,plain,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag,E: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
=> ( ( binDag_Mirabelle_Dag @ A @ B @ C @ E )
=> ( D = E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_subdag__neq) ).
thf(28,plain,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: simpl_ref,D: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ ( binDag476092410e_Node @ B @ C @ D ) )
=> ( ( binDag786255756subdag @ A @ B )
& ( binDag786255756subdag @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_subdag__NodeD) ).
thf(21,plain,
! [A: binDag_Mirabelle_dag,B: binDag_Mirabelle_dag,C: simpl_ref,D: binDag_Mirabelle_dag] :
( ( binDag786255756subdag @ A @ ( binDag476092410e_Node @ B @ C @ D ) )
=> ( ( binDag786255756subdag @ A @ B )
& ( binDag786255756subdag @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag,E: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
=> ( ( binDag786255756subdag @ D @ E )
=> ? [F: simpl_ref] : ( binDag_Mirabelle_Dag @ F @ B @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Dag__subdag) ).
thf(32,plain,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag,E: binDag_Mirabelle_dag] :
( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
=> ( ( binDag786255756subdag @ D @ E )
=> ? [F: simpl_ref] : ( binDag_Mirabelle_Dag @ F @ B @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
binDag786255756subdag @ t @ ( binDag476092410e_Node @ lt @ p @ rt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_subdag) ).
thf(64,plain,
binDag786255756subdag @ t @ ( binDag476092410e_Node @ lt @ p @ rt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
( ( binDag1297733282se_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
= ( B @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_dag_Osimps_I5_J) ).
thf(47,plain,
! [TA: $tType,A: TA,B: binDag_Mirabelle_dag > simpl_ref > binDag_Mirabelle_dag > TA,C: binDag_Mirabelle_dag,D: simpl_ref,E: binDag_Mirabelle_dag] :
( ( binDag1297733282se_dag @ TA @ A @ B @ ( binDag476092410e_Node @ C @ D @ E ) )
= ( B @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag] :
( ( A != simpl_Null )
=> ( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
= ( ? [E: binDag_Mirabelle_dag,F: binDag_Mirabelle_dag] :
( ( D
= ( binDag476092410e_Node @ E @ A @ F ) )
& ( binDag_Mirabelle_Dag @ ( B @ A ) @ B @ C @ E )
& ( binDag_Mirabelle_Dag @ ( C @ A ) @ B @ C @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Dag__Ref) ).
thf(68,plain,
! [A: simpl_ref,B: simpl_ref > simpl_ref,C: simpl_ref > simpl_ref,D: binDag_Mirabelle_dag] :
( ( A != simpl_Null )
=> ( ( binDag_Mirabelle_Dag @ A @ B @ C @ D )
= ( ? [E: binDag_Mirabelle_dag,F: binDag_Mirabelle_dag] :
( ( D
= ( binDag476092410e_Node @ E @ A @ F ) )
& ( binDag_Mirabelle_Dag @ ( B @ A ) @ B @ C @ E )
& ( binDag_Mirabelle_Dag @ ( C @ A ) @ B @ C @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(75,plain,
$false,
inference(e,[status(thm)],[61,65,41,54,35,50,72,40,37,25,20,57,28,21,32,64,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM170^1 : 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
% 0.09/0.21 % Computer : n026.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 17:51:12 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.41/1.20 % [INFO] Parsing done (398ms).
% 2.41/1.21 % [INFO] Running in sequential loop mode.
% 3.31/1.59 % [INFO] eprover registered as external prover.
% 3.53/1.60 % [INFO] Scanning for conjecture ...
% 3.73/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 279 axioms. Running axiom selection ...
% 3.94/1.82 % [INFO] Axiom selection finished. Selected 17 axioms (removed 262 axioms).
% 3.94/1.89 % [INFO] Problem is higher-order (TPTP THF).
% 4.23/1.90 % [INFO] Type checking passed.
% 4.23/1.91 % [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 ...
% 6.21/2.79 % External prover 'e' found a proof!
% 6.21/2.79 % [INFO] Killing All external provers ...
% 6.21/2.79 % Time passed: 2440ms (effective reasoning time: 1574ms)
% 6.21/2.79 % 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)>
% 6.21/2.80 % Axioms used in derivation (17): fact_2_subdag, fact_12_dag_Osimps_I5_J, fact_26_subdag__trans, fact_17_subdag__neq, fact_5_Dag__unique1, fact_6_subdag_Osimps_I2_J, fact_9_Dag__Ref, fact_4_Dag__unique, fact_8_Dag__subdag, fact_3_dag_Oinject, fact_7_subdag__NodeD, fact_10_Dag_Osimps_I2_J, fact_25_subdag__not__sym, fact_1_calculation, fact_11_dag_Osimps_I7_J, fact_0_assms, conj_0
% 6.21/2.80 % No. of inferences in proof: 38
% 6.49/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2440 ms resp. 1574 ms w/o parsing
% 6.49/2.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.49/2.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------