%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX186+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 : n001.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 3.02s 2.34s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 9 ~; 0 |; 0 &; 58 @)
% ( 0 <=>; 3 =>; 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 : 10 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 26 !; 9 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(drop_decl,type,
drop: $i > $i > $i ).
thf(head_decl,type,
head: $i > $i ).
thf(cons_decl,type,
cons: $i > $i > $i ).
thf(tail_decl,type,
tail: $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(proj1S_decl,type,
proj1S: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ s @ drop ) )
= ( C @ ( A @ drop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ cons ) @ ( A @ s @ drop ) )
= ( C @ ( A @ drop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(27,plain,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
? [A: $i,B: $i,C: $i] :
~ ( ( ( B @ ( A @ drop ) )
= ( C @ ( A @ drop ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_009) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i,C: $i] :
~ ( ( ( B @ ( A @ drop ) )
= ( C @ ( A @ drop ) ) )
=> ( B = C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ? [A: $i,B: $i,C: $i] :
~ ( ( ( B @ ( A @ drop ) )
= ( C @ ( A @ drop ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ s )
!= z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(30,plain,
! [A: $i] :
( ( A @ s )
!= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i] :
( ( nil @ ( A @ s @ drop ) )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(34,plain,
! [A: $i] :
( ( nil @ ( A @ s @ drop ) )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ cons ) @ head )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( z @ drop ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( z @ drop ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(23,plain,
! [A: $i,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[37,20,27,11,30,34,17,40,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX186+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
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 16:57:13 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.80/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/1.26 % [INFO] Parsing done (229ms).
% 1.15/1.27 % [INFO] Running in sequential loop mode.
% 1.76/1.76 % [INFO] eprover registered as external prover.
% 1.76/1.78 % [INFO] Scanning for conjecture ...
% 2.04/1.91 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.04/1.94 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.04/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.04/1.97 % [INFO] Type checking passed.
% 2.04/1.97 % [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 ...
% 3.02/2.34 % External prover 'e' found a proof!
% 3.02/2.34 % [INFO] Killing All external provers ...
% 3.02/2.34 % Time passed: 1783ms (effective reasoning time: 1060ms)
% 3.02/2.34 % 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)>
% 3.02/2.34 % Axioms used in derivation (8): axiom_002, axiom_006, axiom_005, axiom_001, axiom_004, axiom_008, axiom_003, axiom_007
% 3.02/2.34 % No. of inferences in proof: 20
% 3.02/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1783 ms resp. 1060 ms w/o parsing
% 3.02/2.39 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.02/2.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------