%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX233_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 : n004.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 09:15:22 AM UTC 2026
% Result : Theorem 3.28s 7.25s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 20 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 10 ~; 0 |; 3 &; 47 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 ^; 22 !; 3 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(cons_decl,type,
cons: $o > $i > $i ).
thf(g_decl,type,
g: $o > $o ).
thf(f_decl,type,
f: $i > $o ).
thf(head_decl,type,
head: $i > $o ).
thf(tail_decl,type,
tail: $i > $i ).
thf(nil_decl,type,
nil: $i ).
thf(h_decl,type,
h: $i > $i ).
thf(6,axiom,
( ( nil @ h )
= nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(37,plain,
( ( nil @ h )
= nil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $o,B: $i] :
( ( B @ ( A @ cons ) @ f )
<=> ~ ( B @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(52,plain,
! [A: $o,B: $i] :
( ( ~ ( B @ f )
=> ( B @ ( A @ cons ) @ f ) )
& ( ( B @ ( A @ cons ) @ f )
=> ~ ( B @ f ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $o] :
( ( A @ g )
<=> ~ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(46,plain,
! [A: $o] :
( ( ~ A
=> ( A @ g ) )
& ( ( A @ g )
=> ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $o,B: $i] :
( ( B @ ( A @ cons ) @ head )
<=> A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(13,plain,
! [A: $o,B: $i] :
( ( A
=> ( B @ ( A @ cons ) @ head ) )
& ( ( B @ ( A @ cons ) @ head )
=> A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $o,B: $i] :
( ( B @ ( A @ cons ) @ h )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(39,plain,
! [A: $o,B: $i] :
( ( B @ ( A @ cons ) @ h )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
? [A: $i] : ( A @ f ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_011) ).
thf(2,negated_conjecture,
~ ? [A: $i] : ( A @ f ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ? [A: $i] : ( A @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
nil @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(51,plain,
nil @ f,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $o,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(28,plain,
! [A: $o,B: $i] :
( nil
!= ( B @ ( A @ cons ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $o,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(21,plain,
! [A: $o,B: $i] :
( ( B @ ( A @ cons ) @ tail )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,plain,
$false,
inference(e,[status(thm)],[37,52,46,13,39,11,51,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX233_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/5.62 % Computer : n004.cluster.edu
% 0.16/5.62 % Model : x86_64 x86_64
% 0.16/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.62 % Memory : 8046.5625MB
% 0.16/5.62 % OS : Linux 6.8.0-71-generic
% 0.16/5.62 % CPULimit : 300
% 0.16/5.62 % WCLimit : 300
% 0.16/5.62 % DateTime : Sat Sep 26 17:00:43 UTC 2026
% 0.16/5.62 % CPUTime :
% 0.16/5.62 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.19/5.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.97/6.04 % [INFO] Parsing done (100ms).
% 0.97/6.06 % [INFO] Running in sequential loop mode.
% 1.58/6.46 % [INFO] eprover registered as external prover.
% 1.58/6.47 % [INFO] Scanning for conjecture ...
% 1.72/6.54 % [WARNING] Symbol 'f' was used without specifying its type first. Assuming default type '$i -> $o' ...
% 1.72/6.57 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 1.91/6.60 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 1.91/6.60 % [WARNING] Symbol 'head' was used without specifying its type first. Assuming default type '$i -> $o' ...
% 1.91/6.61 % [WARNING] Symbol 'tail' was used without specifying its type first. Assuming default type '$i -> $i' ...
% 1.91/6.61 % [WARNING] Symbol 'nil' was used without specifying its type first. Assuming default type '$i' ...
% 1.91/6.62 % [WARNING] Symbol 'h' was used without specifying its type first. Assuming default type '$i -> $i' ...
% 1.91/6.62 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.91/6.63 % [INFO] Type checking passed.
% 1.91/6.63 % [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 ...
% 3.28/7.25 % External prover 'e' found a proof!
% 3.28/7.25 % [INFO] Killing All external provers ...
% 3.28/7.25 % Time passed: 1523ms (effective reasoning time: 1188ms)
% 3.28/7.25 % 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)>
% 3.28/7.25 % Axioms used in derivation (8): axiom_009, axiom_010, axiom_006, axiom_005, axiom_004, axiom_008, axiom_003, axiom_007
% 3.28/7.25 % No. of inferences in proof: 20
% 3.28/7.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1523 ms resp. 1188 ms w/o parsing
% 3.52/7.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.52/7.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------