%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM693_8 : TPTP v9.3.1. Released v8.0.0.
% 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 08:09:39 AM UTC 2026
% Result : Theorem 4.06s 2.52s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 16 unt; 0 typ; 1 def)
% Number of atoms : 48 ( 34 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 105 ( 29 ~; 7 |; 1 &; 62 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 1 ^; 28 !; 1 ?; 31 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(more_decl,type,
more: nat > nat > $o ).
thf(n_1_decl,type,
n_1: nat ).
thf(suc_decl,type,
suc: nat > nat ).
thf(pl_decl,type,
pl: nat > nat > nat ).
thf(sk1_decl,type,
sk1: nat > nat ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: nat] :
@+[B: nat] :
( A
= ( B @ suc ) ) ) ) ).
thf(4,axiom,
! [A: nat] :
( ( A != n_1 )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(13,plain,
! [A: nat] :
( ( A != n_1 )
=> ~ ! [B: nat] :
( A
!= ( B @ suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
! [A: nat] :
( ( A != n_1 )
=> ~ ~ ? [B: nat] :
( A
= ( B @ suc ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
! [A: nat] :
( ( A
= ( A @ sk1 @ suc ) )
| ( A = n_1 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [A: nat] :
( ( ( A @ sk1 @ suc )
= A )
| ( A = n_1 ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(5,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ pl ) @ more ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz18) ).
thf(17,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ pl ) @ more ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,plain,
! [B: nat,A: nat] : ( A @ ( B @ ( A @ pl ) @ more ) ),
inference(cnf,[status(esa)],[17]) ).
thf(1,conjecture,
( ~ ( n_1 @ ( x @ more ) )
=> ( x = n_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24) ).
thf(2,negated_conjecture,
~ ( ~ ( n_1 @ ( x @ more ) )
=> ( x = n_1 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ~ ( n_1 @ ( x @ more ) )
=> ( x = n_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( x != n_1 )
& ~ ( n_1 @ ( x @ more ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
~ ( n_1 @ ( x @ more ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(24,plain,
! [B: nat,A: nat] :
( ( ( A @ ( B @ ( A @ pl ) @ more ) )
!= ( n_1 @ ( x @ more ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,9]) ).
thf(25,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( A @ pl ) @ more ) )
!= ( n_1 @ ( x @ more ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(26,plain,
! [B: nat,A: nat] :
( ( A != n_1 )
| ( ( B @ ( A @ pl ) )
!= x ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
! [A: nat] :
( ( A @ ( n_1 @ pl ) )
!= x ),
inference(simp,[status(thm)],[26]) ).
thf(6,axiom,
! [A: nat] :
( ( A @ suc )
= ( A @ ( n_1 @ pl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4g) ).
thf(19,plain,
! [A: nat] :
( ( A @ suc )
= ( A @ ( n_1 @ pl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,plain,
! [A: nat] :
( ( A @ suc )
= ( A @ ( n_1 @ pl ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [A: nat] :
( ( A @ ( n_1 @ pl ) )
= ( A @ suc ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(28,plain,
! [A: nat] :
( ( A @ suc )
!= x ),
inference(rewrite,[status(thm)],[27,21]) ).
thf(35,plain,
! [B: nat,A: nat] :
( ( ( A @ sk1 @ suc )
!= ( B @ suc ) )
| ( A != x )
| ( A = n_1 ) ),
inference(paramod_ordered,[status(thm)],[16,28]) ).
thf(36,plain,
! [A: nat] :
( ( A != x )
| ( A = n_1 ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( C )),bind(B,$thf( C @ sk1 ))]]) ).
thf(39,plain,
n_1 = x,
inference(simp,[status(thm)],[36]) ).
thf(10,plain,
x != n_1,
inference(cnfConj,[status(thm)],[8]) ).
thf(11,plain,
n_1 != x,
inference(lifteq,[status(thm)],[10]) ).
thf(40,plain,
$false,
inference(simplifyReflect,[status(thm)],[39,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM693_8 : TPTP v9.3.1. Released v8.0.0.
% 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
% 0.15/0.42 % Computer : n017.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 03:42:33 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 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
% 0.87/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.19 % [INFO] Parsing done (182ms).
% 1.40/1.21 % [INFO] Running in sequential loop mode.
% 1.99/1.62 % [INFO] eprover registered as external prover.
% 1.99/1.62 % [INFO] Scanning for conjecture ...
% 2.17/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.17/1.75 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.17/1.77 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.17/1.78 % [INFO] Type checking passed.
% 2.17/1.78 % [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 ...
% 4.06/2.51 % [INFO] Killing All external provers ...
% 4.06/2.51 % Time passed: 1941ms (effective reasoning time: 1294ms)
% 4.06/2.51 % 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)>
% 4.06/2.51 % Axioms used in derivation (3): satz3, satz18, satz4g
% 4.06/2.51 % No. of inferences in proof: 28
% 4.06/2.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1941 ms resp. 1294 ms w/o parsing
% 4.06/2.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.06/2.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------