%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX217-1 : 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 : n006.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 09:15:19 AM UTC 2026
% Result : Unsatisfiable 3.74s 7.58s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 65 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 65 ( 64 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 230 ( 2 ~; 0 |; 0 &; 228 @)
% ( 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 : 24 ( 22 usr; 7 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(sat_comm_decl,type,
sat_comm: $i > $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(append_decl,type,
append: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(double_decl,type,
double: $i > $i ).
thf(addNat_decl,type,
addNat: $i > $i > $i ).
thf(rd_decl,type,
rd: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(x_decl,type,
x: $i > $i > $i ).
thf(shw_decl,type,
shw: $i > $i ).
thf(suc_decl,type,
suc: $i > $i ).
thf(aux_decl,type,
aux: $i > $i > $i ).
thf(evenNat_decl,type,
evenNat: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(half_decl,type,
half: $i > $i ).
thf(o_decl,type,
o: $i ).
thf(i_decl,type,
i: $i ).
thf(notb_decl,type,
notb: $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(eq3_decl,type,
eq3: $i > $i > $i ).
thf(28,axiom,
( ( i @ ( o @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
thf(88,plain,
( ( i @ ( o @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( o @ cons ) @ rd )
= ( A @ rd @ double ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( o @ cons ) @ rd )
= ( A @ rd @ double ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ x ) )
= ( B @ shw @ ( A @ shw @ append ) @ rd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ x ) )
= ( B @ shw @ ( A @ shw @ append ) @ rd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
( ( zero @ half )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(52,plain,
( ( zero @ half )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
thf(84,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
thf(74,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( i @ cons ) @ rd )
= ( A @ rd @ double @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
thf(60,plain,
! [A: $i] :
( ( A @ ( i @ cons ) @ rd )
= ( A @ rd @ double @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ sat_comm ) )
= ( A @ ( B @ x ) @ ( B @ ( A @ x ) @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sat_comm ) )
= ( A @ ( B @ x ) @ ( B @ ( A @ x ) @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
( ( o @ ( i @ eq3 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
thf(96,plain,
( ( o @ ( i @ eq3 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ suc @ evenNat )
= ( A @ evenNat @ notb ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(64,plain,
! [A: $i] :
( ( A @ suc @ evenNat )
= ( A @ evenNat @ notb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ suc @ shw )
= ( A @ suc @ evenNat @ ( A @ aux ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(44,plain,
! [A: $i] :
( ( A @ suc @ shw )
= ( A @ suc @ evenNat @ ( A @ aux ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,axiom,
( ( btrue @ notb )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(76,plain,
( ( btrue @ notb )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ suc @ ( A @ suc @ eq ) )
= ( B @ ( A @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ suc @ ( A @ suc @ eq ) )
= ( B @ ( A @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
thf(80,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
( ( zero @ suc @ half )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(48,plain,
( ( zero @ suc @ half )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
( ( zero @ shw )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(50,plain,
( ( zero @ shw )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
( ( bfalse @ notb )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(72,plain,
( ( bfalse @ notb )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
( ( nil @ rd )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
thf(40,plain,
( ( nil @ rd )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( nil @ append ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( nil @ append ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,axiom,
( ( zero @ evenNat )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(94,plain,
( ( zero @ evenNat )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(29,axiom,
! [A: $i] :
( ( bfalse @ ( A @ aux ) )
= ( A @ suc @ half @ shw @ ( i @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(90,plain,
! [A: $i] :
( ( bfalse @ ( A @ aux ) )
= ( A @ suc @ half @ shw @ ( i @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ cons ) @ append ) )
= ( C @ ( B @ append ) @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(46,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)],[7]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ suc @ ( zero @ eq ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
thf(78,plain,
! [A: $i] :
( ( A @ suc @ ( zero @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ double )
= ( A @ ( A @ addNat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(38,plain,
! [A: $i] :
( ( A @ double )
= ( A @ ( A @ addNat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,axiom,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
thf(70,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ sat_comm ) @ eq2 ) )
!= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( bfalse @ ( B @ ( A @ sat_comm ) @ eq2 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ suc @ suc @ half )
= ( A @ half @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(54,plain,
! [A: $i] :
( ( A @ suc @ suc @ half )
= ( A @ half @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,axiom,
! [A: $i] :
( ( btrue @ ( A @ aux ) )
= ( A @ suc @ half @ shw @ ( o @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(86,plain,
! [A: $i] :
( ( btrue @ ( A @ aux ) )
= ( A @ suc @ half @ shw @ ( o @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ suc @ addNat ) )
= ( B @ ( A @ addNat ) @ suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ suc @ addNat ) )
= ( B @ ( A @ addNat ) @ suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( A @ eq3 ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( A @ eq3 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [A: $i] :
( ( zero @ ( A @ suc @ eq ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
thf(68,plain,
! [A: $i] :
( ( zero @ ( A @ suc @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( zero @ addNat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(62,plain,
! [A: $i] :
( ( A @ ( zero @ addNat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,plain,
$false,
inference(e,[status(thm)],[88,56,42,52,84,74,60,92,96,64,44,76,66,80,48,50,72,40,36,94,90,46,78,38,70,33,54,86,58,82,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX217-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.13 % 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
% 0.23/5.50 % Computer : n006.cluster.edu
% 0.23/5.50 % Model : x86_64 x86_64
% 0.23/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/5.50 % Memory : 8046.5625MB
% 0.23/5.50 % OS : Linux 6.8.0-71-generic
% 0.26/5.50 % CPULimit : 300
% 0.26/5.50 % WCLimit : 300
% 0.26/5.50 % DateTime : Sat Sep 26 16:57:48 UTC 2026
% 0.26/5.50 % CPUTime :
% 0.26/5.50 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
% 1.00/6.08 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/6.28 % [INFO] Parsing done (188ms).
% 1.28/6.29 % [INFO] Running in sequential loop mode.
% 2.12/6.70 % [INFO] eprover registered as external prover.
% 2.12/6.71 % [INFO] Scanning for conjecture ...
% 2.29/6.80 % [INFO] Found a conjecture (or negated_conjecture) and 31 axioms. Running axiom selection ...
% 2.29/6.88 % [INFO] Axiom selection finished. Selected 31 axioms (removed 0 axioms).
% 2.44/6.91 % [INFO] Problem is propositional (TPTP CNF).
% 2.44/6.92 % [INFO] Type checking passed.
% 2.44/6.92 % [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 ...
% 3.74/7.57 % External prover 'e' found a proof!
% 3.74/7.57 % [INFO] Killing All external provers ...
% 3.74/7.57 % Time passed: 1933ms (effective reasoning time: 1276ms)
% 3.74/7.58 % Axioms used in derivation (31): 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_015, axiom_004, axiom, axiom_011, axiom_026, axiom_020, axiom_019, axiom_008
% 3.74/7.58 % No. of inferences in proof: 65
% 3.74/7.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1933 ms resp. 1276 ms w/o parsing
% 4.09/7.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.09/7.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------