%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX187+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 : 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 09:15:13 AM UTC 2026
% Result : Theorem 4.30s 2.64s
% Output : Refutation 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 36 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 194 ( 16 ~; 0 |; 1 &; 159 @)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 46 !; 12 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(x2_decl,type,
x2: $i > $i > $o ).
thf(length_decl,type,
length: $i > $i ).
thf(rotate_decl,type,
rotate: $i > $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(x_decl,type,
x: $i > $i > $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(proj1S_decl,type,
proj1S: $i > $i ).
thf(13,axiom,
( ( nil @ length )
= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(57,plain,
( ( nil @ length )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(65,plain,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
~ ( z @ ( z @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(40,plain,
~ ( z @ ( z @ x2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
? [A: $i,B: $i,C: $i,D: $i] :
~ ( ( D @ length @ ( A @ x2 ) )
=> ( ( C @ length @ ( B @ x2 ) )
=> ( ( D = C )
=> ( ( ( D @ ( z @ s @ rotate ) )
!= D )
=> ( ( ( D @ ( A @ rotate ) )
= ( C @ ( B @ rotate ) ) )
=> ( A = B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_017) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i,C: $i,D: $i] :
~ ( ( D @ length @ ( A @ x2 ) )
=> ( ( C @ length @ ( B @ x2 ) )
=> ( ( D = C )
=> ( ( ( D @ ( z @ s @ rotate ) )
!= D )
=> ( ( ( D @ ( A @ rotate ) )
= ( C @ ( B @ rotate ) ) )
=> ( A = B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ? [A: $i,B: $i,C: $i,D: $i] :
~ ( ( D @ length @ ( A @ x2 ) )
=> ( ( C @ length @ ( B @ x2 ) )
=> ( ( D = C )
=> ( ( ( D @ ( z @ s @ rotate ) )
!= D )
=> ( ( ( D @ ( A @ rotate ) )
= ( C @ ( B @ rotate ) ) )
=> ( A = B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] : ( A @ s @ ( z @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(42,plain,
! [A: $i] : ( A @ s @ ( z @ x2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( nil @ x ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( nil @ x ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ s @ ( A @ s @ x2 ) )
<=> ( B @ ( A @ x2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ x2 ) )
=> ( B @ s @ ( A @ s @ x2 ) ) )
& ( ( B @ s @ ( A @ s @ x2 ) )
=> ( B @ ( A @ x2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ length )
= ( B @ length @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ length )
= ( B @ length @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(27,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( z @ rotate ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
thf(71,plain,
! [A: $i] :
( ( A @ ( z @ rotate ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( nil @ ( A @ s @ rotate ) )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
thf(54,plain,
! [A: $i] :
( ( nil @ ( A @ s @ rotate ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ s )
!= z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(50,plain,
! [A: $i] :
( ( A @ s )
!= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ cons ) @ x ) )
= ( A @ ( C @ x ) @ ( B @ cons ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ cons ) @ x ) )
= ( A @ ( C @ x ) @ ( B @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ s @ rotate ) )
= ( nil @ ( B @ cons ) @ ( C @ x ) @ ( A @ rotate ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ s @ rotate ) )
= ( nil @ ( B @ cons ) @ ( C @ x ) @ ( A @ rotate ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
! [A: $i] :
~ ( z @ ( A @ s @ x2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(62,plain,
! [A: $i] :
~ ( z @ ( A @ s @ x2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(81,plain,
$false,
inference(e,[status(thm)],[57,65,34,40,19,42,24,37,44,59,27,71,54,50,31,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX187+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
% 0.15/0.41 % Computer : n006.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 16:50:41 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.18 % [INFO] Parsing done (189ms).
% 1.26/1.20 % [INFO] Running in sequential loop mode.
% 2.03/1.60 % [INFO] eprover registered as external prover.
% 2.03/1.61 % [INFO] Scanning for conjecture ...
% 2.21/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.21/1.79 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.39/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.82 % [INFO] Type checking passed.
% 2.39/1.82 % [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 ...
% 4.30/2.64 % External prover 'e' found a proof!
% 4.30/2.64 % [INFO] Killing All external provers ...
% 4.30/2.64 % Time passed: 2092ms (effective reasoning time: 1438ms)
% 4.30/2.64 % 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)>
% 4.30/2.64 % Axioms used in derivation (16): axiom_009, axiom_010, axiom_002, axiom_016, axiom_005, axiom_012, axiom_001, axiom_011, axiom_008, axiom_003, axiom_014, axiom_007, axiom_013, axiom_006, axiom_015, axiom_004
% 4.30/2.64 % No. of inferences in proof: 36
% 4.30/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2092 ms resp. 1438 ms w/o parsing
% 4.70/2.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.70/2.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------