%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 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 : 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 09:15:21 AM UTC 2026
% Result : Unsatisfiable 3.66s 2.54s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 53 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 57 ( 56 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 242 ( 6 ~; 4 |; 0 &; 232 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 86 ( 0 ^; 86 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq3_decl,type,
eq3: $i > $i > $i ).
thf(prop_union_comm_decl,type,
prop_union_comm: $i > $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(elem_decl,type,
elem: $i > $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(barbar_decl,type,
barbar: $i > $i > $i ).
thf(eqNat_decl,type,
eqNat: $i > $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(aux_decl,type,
aux: $i > $i > $i > $i > $i ).
thf(z_decl,type,
z: $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(21,axiom,
! [A: $i] :
( ( A @ s @ ( z @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(69,plain,
! [A: $i] :
( ( A @ s @ ( z @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(8,axiom,
! [A: $i] :
( ( nil @ ( A @ elem ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(42,plain,
! [A: $i] :
( ( nil @ ( A @ elem ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(61,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cons ) @ union ) )
= ( C @ ( A @ elem ) @ ( B @ ( A @ ( C @ aux ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cons ) @ union ) )
= ( C @ ( A @ elem ) @ ( B @ ( A @ ( C @ aux ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( nil @ ( B @ ( A @ cons ) @ eq ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( nil @ ( B @ ( A @ cons ) @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( A @ ( C @ union ) @ ( B @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( bfalse @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( A @ ( C @ union ) @ ( B @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
( ( bfalse @ ( btrue @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(73,plain,
( ( bfalse @ ( btrue @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( A @ eq3 ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(71,plain,
! [A: $i] :
( ( A @ ( A @ eq3 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ prop_union_comm ) )
= ( A @ ( B @ union ) @ ( B @ ( A @ union ) @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ prop_union_comm ) )
= ( A @ ( B @ union ) @ ( B @ ( A @ union ) @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ s @ ( z @ eqNat ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(67,plain,
! [A: $i] :
( ( A @ s @ ( z @ eqNat ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ eq ) )
= bfalse )
| ( ( B @ ( A @ eq2 ) )
!= bfalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ eq ) )
= bfalse )
| ( ( B @ ( A @ eq2 ) )
!= bfalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
( ( btrue @ ( bfalse @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(46,plain,
( ( btrue @ ( bfalse @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( nil @ eq ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ cons ) @ ( nil @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i] :
( ( z @ ( A @ s @ eqNat ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(78,plain,
! [A: $i] :
( ( z @ ( A @ s @ eqNat ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
= ( C @ ( A @ elem ) @ ( B @ ( A @ eqNat ) @ barbar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ cons ) @ ( A @ elem ) )
= ( C @ ( A @ elem ) @ ( B @ ( A @ eqNat ) @ barbar ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eqNat ) )
= ( B @ ( A @ eqNat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eqNat ) )
= ( B @ ( A @ eqNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( bfalse @ barbar ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( bfalse @ barbar ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( A @ ( C @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( btrue @ ( C @ ( B @ ( A @ aux ) ) ) )
= ( A @ ( C @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ prop_union_comm ) @ eq3 ) )
!= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ prop_union_comm ) @ eq3 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ eq ) )
= ( D @ ( C @ eq ) ) )
| ( ( B @ ( A @ eq2 ) )
!= btrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ cons ) @ ( C @ ( A @ cons ) @ eq ) )
= ( D @ ( C @ eq ) ) )
| ( ( B @ ( A @ eq2 ) )
!= btrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( btrue @ barbar ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( btrue @ barbar ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
( ( z @ ( z @ eqNat ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(40,plain,
( ( z @ ( z @ eqNat ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i] :
( ( z @ ( A @ s @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(55,plain,
! [A: $i] :
( ( z @ ( A @ s @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( nil @ union ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( nil @ union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq2 ) )
= ( B @ ( A @ eq2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq2 ) )
= ( B @ ( A @ eq2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,plain,
$false,
inference(e,[status(thm)],[69,42,61,38,65,53,73,71,80,67,75,46,57,78,32,34,44,59,27,48,63,40,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % 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
% 0.15/0.51 % Computer : n018.cluster.edu
% 0.15/0.51 % Model : x86_64 x86_64
% 0.15/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.51 % Memory : 8046.5625MB
% 0.15/0.51 % OS : Linux 6.8.0-71-generic
% 0.15/0.51 % CPULimit : 300
% 0.15/0.51 % WCLimit : 300
% 0.15/0.51 % DateTime : Sat Sep 26 17:02:37 UTC 2026
% 0.15/0.51 % CPUTime :
% 0.15/0.51 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
% 0.91/1.11 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.31 % [INFO] Parsing done (192ms).
% 1.39/1.32 % [INFO] Running in sequential loop mode.
% 2.01/1.72 % [INFO] eprover registered as external prover.
% 2.01/1.73 % [INFO] Scanning for conjecture ...
% 2.17/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 25 axioms. Running axiom selection ...
% 2.17/1.89 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 2.33/1.92 % [INFO] Problem is propositional (TPTP CNF).
% 2.33/1.93 % [INFO] Type checking passed.
% 2.33/1.93 % [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 ...
% 3.66/2.54 % External prover 'e' found a proof!
% 3.66/2.54 % [INFO] Killing All external provers ...
% 3.66/2.54 % Time passed: 1872ms (effective reasoning time: 1211ms)
% 3.66/2.54 % Axioms used in derivation (25): axiom_024, axiom_010, axiom_021, axiom_002, axiom_023, axiom_016, axiom_005, axiom_012, axiom_001, axiom_022, axiom_020, axiom_003, axiom_014, axiom_007, axiom_018, axiom_009, axiom_017, axiom_013, axiom_006, axiom_015, axiom_004, axiom, axiom_011, axiom_019, axiom_008
% 3.66/2.54 % No. of inferences in proof: 53
% 3.66/2.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1872 ms resp. 1211 ms w/o parsing
% 4.00/2.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.00/2.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------