%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX200+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 : n007.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 : Theorem 4.37s 2.77s
% Output : Refutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 18 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 212 ( 16 ~; 0 |; 5 &; 175 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 ^; 54 !; 6 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(ord_decl,type,
ord: $i > $o ).
thf(merge_decl,type,
merge: $i > $i > $i ).
thf(proj1S_decl,type,
proj1S: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(head_decl,type,
head: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(leqNat_decl,type,
leqNat: $i > $i > $o ).
thf(4,axiom,
! [A: $i] :
( z
!= ( A @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(24,plain,
! [A: $i] :
( z
!= ( A @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i] : ( nil @ ( A @ cons ) @ ord ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
thf(57,plain,
! [A: $i] : ( nil @ ( A @ cons ) @ ord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ leqNat ) )
=> ( ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ merge ) )
= ( D @ ( C @ cons ) @ ( B @ merge ) @ ( A @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(53,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( A @ leqNat ) )
=> ( ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ merge ) )
= ( D @ ( C @ cons ) @ ( B @ merge ) @ ( A @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ s @ leqNat ) )
<=> ( B @ ( A @ leqNat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ leqNat ) )
=> ( B @ s @ ( A @ s @ leqNat ) ) )
& ( ( B @ s @ ( A @ s @ leqNat ) )
=> ( B @ ( A @ leqNat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( nil @ ( B @ ( A @ cons ) @ merge ) )
= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( nil @ ( B @ ( A @ cons ) @ merge ) )
= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( A @ leqNat ) )
=> ( ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ merge ) )
= ( D @ ( B @ ( A @ cons ) @ merge ) @ ( C @ cons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
thf(49,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( A @ leqNat ) )
=> ( ( D @ ( C @ cons ) @ ( B @ ( A @ cons ) @ merge ) )
= ( D @ ( B @ ( A @ cons ) @ merge ) @ ( C @ cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ cons ) @ ord )
<=> ( ( C @ ( B @ cons ) @ ord )
& ( B @ ( A @ leqNat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ cons ) @ ord )
& ( B @ ( A @ leqNat ) ) )
=> ( C @ ( B @ cons ) @ ( A @ cons ) @ ord ) )
& ( ( C @ ( B @ cons ) @ ( A @ cons ) @ ord )
=> ( ( C @ ( B @ cons ) @ ord )
& ( B @ ( A @ leqNat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(35,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(31,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(21,plain,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
~ ( z @ ( A @ s @ leqNat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(38,plain,
! [A: $i] :
~ ( z @ ( A @ s @ leqNat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( nil @ merge ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( nil @ merge ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
~ ( ( A @ ord )
=> ( ~ ( B @ ord )
=> ( B @ ( A @ merge ) @ ord ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_016) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
~ ( ( A @ ord )
=> ( ~ ( B @ ord )
=> ( B @ ( A @ merge ) @ ord ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ? [A: $i,B: $i] :
~ ( ( A @ ord )
=> ( ~ ( B @ ord )
=> ( B @ ( A @ merge ) @ ord ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i] : ( A @ ( z @ leqNat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(47,plain,
! [A: $i] : ( A @ ( z @ leqNat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
nil @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
thf(62,plain,
nil @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(73,plain,
$false,
inference(e,[status(thm)],[24,57,53,41,59,49,66,35,31,21,28,38,63,18,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX200+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.11 % 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
% 0.24/0.49 % Computer : n007.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 16:52:40 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 0.93/1.05 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.24 % [INFO] Parsing done (193ms).
% 1.43/1.26 % [INFO] Running in sequential loop mode.
% 2.06/1.68 % [INFO] eprover registered as external prover.
% 2.06/1.69 % [INFO] Scanning for conjecture ...
% 2.26/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.46/1.86 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.46/1.89 % [INFO] Problem is first-order (TPTP FOF).
% 2.46/1.89 % [INFO] Type checking passed.
% 2.68/1.90 % [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 ...
% 4.37/2.77 % External prover 'e' found a proof!
% 4.37/2.77 % [INFO] Killing All external provers ...
% 4.37/2.77 % Time passed: 2132ms (effective reasoning time: 1503ms)
% 4.37/2.77 % 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)>
% 4.37/2.77 % Axioms used in derivation (15): axiom_009, axiom_010, axiom_002, axiom_005, axiom_012, axiom_001, axiom_011, axiom_008, axiom_003, axiom_014, axiom_007, axiom_013, axiom_006, axiom_015, axiom_004
% 4.37/2.77 % No. of inferences in proof: 34
% 4.37/2.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2132 ms resp. 1503 ms w/o parsing
% 4.62/2.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.62/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------