%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM637^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n009.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 : Wed Sep 30 08:17:51 AM UTC 2026
% Result : Theorem 39.59s 12.69s
% Output : Refutation 34.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 59 ( 55 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 169 ( 54 ~; 27 |; 4 &; 75 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 13 ^; 29 !; 4 ?; 48 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(one_decl,type,
one: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk3_decl,type,
sk3: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A != one )
=> ? [B: $i] :
( A
= ( succ @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $o] :
@+[B: $i] :
~ ( ( A @ B )
=> ( A @ ( succ @ B ) ) ) ) ) ).
thf(5,axiom,
! [A: $i > $o] :
( ( ( A @ one )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( succ @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
thf(21,plain,
! [A: $i > $o] :
( ( ( A @ one )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( succ @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
! [B: $i,A: $i > $o] :
( ( ~ ( A @ one )
| ( A @ ( sk3 @ A ) )
| ( A @ B ) )
& ( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( A @ B ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(24,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(40,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ one )
| ~ ~ ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[24:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(65,plain,
! [B: $i > $o,A: $i] :
( ( B @ one )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[40]) ).
thf(66,plain,
! [B: $i > $o,A: $i] :
( ( B @ one )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[65]) ).
thf(4002,plain,
! [B: $i > $o,A: $i] :
( ( B @ one )
| ~ ( B @ A )
| ( ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
!= ( B @ one ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[66]) ).
thf(4062,plain,
! [A: $i] :
( ( A = one )
| ( A != A )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[4002:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).
thf(4063,plain,
! [A: $i] :
( ( A = one )
| ( A != A )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ~ $true ),
inference(lifteq,[status(thm)],[4062]) ).
thf(4274,plain,
! [A: $i] :
( ( A = one )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) ) ),
inference(simp,[status(thm)],[4063]) ).
thf(1,conjecture,
! [A: $i] :
( ( A != one )
=> ? [B: $i] :
( A
= ( succ @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A != one )
=> ? [B: $i] :
( A
= ( succ @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ( A != one )
=> ? [B: $i] :
( A
= ( succ @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
! [A: $i] :
( ( sk1 != one )
& ( sk1
!= ( succ @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
sk1 != one,
inference(cnfConj,[status(thm)],[7]) ).
thf(10,plain,
sk1 != one,
inference(lifteq,[status(thm)],[8]) ).
thf(8498,plain,
! [A: $i] :
( ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ( one != one )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[4274,10]) ).
thf(8499,plain,
! [A: $i] :
( ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[8498]) ).
thf(8500,plain,
( ( sk1
= ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) ) )
!= ( sk1 = one ) ),
inference(pattern_uni,[status(thm)],[8499:[bind(A,$thf( sk1 ))]]) ).
thf(9320,plain,
( ( sk1
= ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) ) )
| ( sk1 = one ) ),
inference(bool_ext,[status(thm)],[8500]) ).
thf(9374,plain,
( ( ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) )
= sk1 )
| ( sk1 = one ) ),
inference(lifteq,[status(thm)],[9320]) ).
thf(9,plain,
! [A: $i] :
( sk1
!= ( succ @ A ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(11,plain,
! [A: $i] :
( ( succ @ A )
!= sk1 ),
inference(lifteq,[status(thm)],[9]) ).
thf(9416,plain,
$false,
inference(simplifyReflect,[status(thm)],[9374,10,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM637^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 12:11:00 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (184ms).
% 1.20/1.00 % [INFO] Running in sequential loop mode.
% 1.77/1.38 % [INFO] eprover registered as external prover.
% 1.77/1.39 % [INFO] Scanning for conjecture ...
% 1.94/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.10/1.51 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.10/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.52 % [INFO] Type checking passed.
% 2.10/1.53 % [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 ...
% 39.59/12.68 % [INFO] Killing All external provers ...
% 39.59/12.69 % Time passed: 12347ms (effective reasoning time: 11679ms)
% 39.59/12.69 % 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)>
% 39.59/12.69 % Axioms used in derivation (1): induction
% 39.59/12.69 % No. of inferences in proof: 25
% 39.59/12.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12347 ms resp. 11679 ms w/o parsing
% 34.04/12.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.04/12.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------