%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX206-1 : 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 : n017.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 09:15:17 AM UTC 2026
% Result : Unsatisfiable 4.92s 3.14s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 27 ( 26 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 90 ( 2 ~; 0 |; 0 &; 88 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 26 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(eq2_decl,type,
eq2: $i > $i > $i ).
thf(plus_not_idem_decl,type,
plus_not_idem: $i > $i ).
thf(bfalse_decl,type,
bfalse: $i ).
thf(btrue_decl,type,
btrue: $i ).
thf(impl_decl,type,
impl: $i > $i > $i ).
thf(x2_decl,type,
x2: $i > $i > $i ).
thf(z_decl,type,
z: $i ).
thf(s_decl,type,
s: $i > $i ).
thf(eq_decl,type,
eq: $i > $i > $i ).
thf(1,negated_conjecture,
! [A: $i] :
( ( bfalse @ ( A @ plus_not_idem @ eq2 ) )
!= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(14,plain,
! [A: $i] :
( ( bfalse @ ( A @ plus_not_idem @ eq2 ) )
!= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(29,plain,
( ( bfalse @ ( btrue @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( btrue @ impl ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(27,plain,
( ( btrue @ ( bfalse @ eq2 ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( A @ eq2 ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
thf(35,plain,
! [A: $i] :
( ( z @ ( A @ s @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ s @ ( A @ s @ eq ) )
= ( B @ ( A @ eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ s @ x2 ) )
= ( B @ ( A @ x2 ) @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ s @ x2 ) )
= ( B @ ( A @ x2 ) @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( bfalse @ impl ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( A @ eq ) )
= btrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ plus_not_idem )
= ( bfalse @ ( btrue @ eq2 ) @ ( A @ ( A @ ( A @ x2 ) @ eq ) @ impl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(25,plain,
! [A: $i] :
( ( A @ plus_not_idem )
= ( bfalse @ ( btrue @ eq2 ) @ ( A @ ( A @ ( A @ x2 ) @ eq ) @ impl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( z @ x2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( z @ x2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
thf(33,plain,
! [A: $i] :
( ( A @ s @ ( z @ eq ) )
= bfalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[14,29,17,27,39,35,31,23,19,37,25,21,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX206-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.12 % 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
% 0.23/0.48 % Computer : n017.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sat Sep 26 16:50:49 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.44/1.32 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.79/1.57 % [INFO] Parsing done (253ms).
% 1.79/1.60 % [INFO] Running in sequential loop mode.
% 2.81/2.19 % [INFO] eprover registered as external prover.
% 2.92/2.21 % [INFO] Scanning for conjecture ...
% 3.09/2.33 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 3.09/2.38 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 3.25/2.40 % [INFO] Problem is propositional (TPTP CNF).
% 3.25/2.41 % [INFO] Type checking passed.
% 3.25/2.41 % [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 ...
% 4.92/3.14 % External prover 'e' found a proof!
% 4.92/3.14 % [INFO] Killing All external provers ...
% 4.92/3.14 % Time passed: 2447ms (effective reasoning time: 1534ms)
% 4.92/3.14 % Axioms used in derivation (12): axiom_009, axiom_010, axiom_002, axiom_006, axiom_005, axiom_001, axiom_004, axiom_008, axiom_003, axiom_007, axiom, axiom_011
% 4.92/3.14 % No. of inferences in proof: 27
% 4.92/3.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2447 ms resp. 1534 ms w/o parsing
% 5.10/3.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.10/3.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------