%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX203-1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n011.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 09:15:16 AM UTC 2026
% Result : Unsatisfiable 15.48s 5.64s
% Output : Refutation 16.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 33
% Syntax : Number of formulae : 67 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 66 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 272 ( 2 ~; 0 |; 0 &; 270 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 0 ^; 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(psorted_rev_decl,type,
psorted_rev: $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(elemNat_decl,type,
elemNat: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(orb_decl,type,
orb: $i > $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(append_decl,type,
append: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(lengthNat_decl,type,
lengthNat: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(leqNat_decl,type,
leqNat: $i > $i > $i ).
thf(rev_decl,type,
rev: $i > $i ).
thf(sorted_decl,type,
sorted: $i > $i ).
thf(andb_decl,type,
andb: $i > $i > $i ).
thf(unique_decl,type,
unique: $i > $i ).
thf(aux_decl,type,
aux: $i > $i > $i > $i ).
thf(impl_decl,type,
impl: $i > $i > $i ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
thf(69,plain,
! [A: $i] :
( ( A @ ( bfalse @ andb ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elemNat ) )
= ( C @ ( A @ elemNat ) @ ( B @ ( A @ eq ) @ orb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elemNat ) )
= ( C @ ( A @ elemNat ) @ ( B @ ( A @ eq ) @ orb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ aux ) ) )
= ( B @ unique ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ aux ) ) )
= ( B @ unique ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ unique )
= ( B @ ( A @ elemNat ) @ ( B @ ( A @ aux ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ unique )
= ( B @ ( A @ elemNat ) @ ( B @ ( A @ aux ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
thf(77,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( nil @ append ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( nil @ append ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
thf(73,plain,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
thf(59,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(29,axiom,
! [A: $i] :
( ( nil @ ( A @ cons ) @ sorted )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
thf(91,plain,
! [A: $i] :
( ( nil @ ( A @ cons ) @ sorted )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
! [A: $i] :
( ( nil @ ( A @ elemNat ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(67,plain,
! [A: $i] :
( ( nil @ ( A @ elemNat ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
( ( nil @ lengthNat )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(43,plain,
( ( nil @ lengthNat )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cons ) @ append ) )
= ( C @ ( B @ append ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cons ) @ append ) )
= ( C @ ( B @ append ) @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
( ( nil @ unique )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(75,plain,
( ( nil @ unique )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ cons ) @ sorted )
= ( C @ ( B @ cons ) @ sorted @ ( B @ ( A @ leqNat ) @ andb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ cons ) @ sorted )
= ( C @ ( B @ cons ) @ sorted @ ( B @ ( A @ leqNat ) @ andb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ( btrue @ orb ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(79,plain,
! [A: $i] :
( ( A @ ( btrue @ orb ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leqNat ) )
= ( B @ ( A @ leqNat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ leqNat ) )
= ( B @ ( A @ leqNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,axiom,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
thf(83,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(93,plain,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(12,axiom,
( ( nil @ rev )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
thf(57,plain,
( ( nil @ rev )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( btrue @ andb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
thf(61,plain,
! [A: $i] :
( ( A @ ( btrue @ andb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,axiom,
( ( nil @ sorted )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
thf(89,plain,
( ( nil @ sorted )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ psorted_rev )
= ( btrue @ ( z @ s @ s @ s @ ( A @ lengthNat @ leqNat ) @ eq2 ) @ ( btrue @ ( A @ unique @ eq2 ) @ impl ) @ ( btrue @ ( A @ rev @ sorted @ eq2 ) @ impl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
thf(65,plain,
! [A: $i] :
( ( A @ psorted_rev )
= ( btrue @ ( z @ s @ s @ s @ ( A @ lengthNat @ leqNat ) @ eq2 ) @ ( btrue @ ( A @ unique @ eq2 ) @ impl ) @ ( btrue @ ( A @ rev @ sorted @ eq2 ) @ impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ( z @ leqNat ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(97,plain,
! [A: $i] :
( ( A @ ( z @ leqNat ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( bfalse @ ( A @ psorted_rev @ eq2 ) )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(34,plain,
! [A: $i] :
( ( bfalse @ ( A @ psorted_rev @ eq2 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ lengthNat )
= ( B @ lengthNat @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ lengthNat )
= ( B @ lengthNat @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ ( bfalse @ orb ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(71,plain,
! [A: $i] :
( ( A @ ( bfalse @ orb ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ rev @ append ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ rev )
= ( nil @ ( A @ cons ) @ ( B @ rev @ append ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
thf(81,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
thf(63,plain,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
! [A: $i] :
( ( z @ ( A @ s @ leqNat ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(95,plain,
! [A: $i] :
( ( z @ ( A @ s @ leqNat ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( btrue @ ( B @ ( A @ aux ) ) )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( btrue @ ( B @ ( A @ aux ) ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(87,plain,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(536,plain,
$false,
inference(e,[status(thm)],[69,37,85,53,77,41,73,59,91,67,43,55,75,51,79,47,83,93,57,61,89,65,97,34,45,71,49,81,39,63,95,99,87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX203-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % 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
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 16:55:44 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 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
% 1.33/1.22 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.43 % [INFO] Parsing done (204ms).
% 1.75/1.45 % [INFO] Running in sequential loop mode.
% 2.85/2.08 % [INFO] eprover registered as external prover.
% 2.85/2.10 % [INFO] Scanning for conjecture ...
% 3.15/2.25 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 3.29/2.37 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 3.49/2.43 % [INFO] Problem is propositional (TPTP CNF).
% 3.49/2.43 % [INFO] Type checking passed.
% 3.49/2.44 % [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 ...
% 15.48/5.63 % External prover 'e' found a proof!
% 15.48/5.63 % [INFO] Killing All external provers ...
% 15.48/5.64 % Time passed: 4980ms (effective reasoning time: 4184ms)
% 15.48/5.64 % Axioms used in derivation (32): axiom_024, axiom_010, axiom_021, axiom_002, axiom_028, axiom_023, axiom_005, axiom_012, axiom_001, axiom_022, axiom_030, axiom_029, axiom_025, axiom_003, axiom_014, axiom_007, axiom_018, axiom_009, axiom_017, axiom_013, axiom_006, axiom_016, axiom_027, axiom_031, axiom_015, axiom_004, axiom, axiom_011, axiom_026, axiom_020, axiom_019, axiom_008
% 15.48/5.64 % No. of inferences in proof: 67
% 15.48/5.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4980 ms resp. 4184 ms w/o parsing
% 16.06/5.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.06/5.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------