%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM636^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:17:50 AM UTC 2026
% Result : Theorem 49.24s 14.38s
% Output : Refutation 42.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 25 unt; 0 typ; 3 def)
% Number of atoms : 103 ( 99 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 261 ( 80 ~; 47 |; 3 &; 124 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 79 ( 18 ^; 55 !; 3 ?; 79 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(one_decl,type,
one: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( succ @ A )
= A ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] :
! [B: $i] :
( ( A @ ( succ @ B ) )
= 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/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(19,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(20,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)],[19]) ).
thf(22,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(43,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ one )
| ~ ~ ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[22:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(80,plain,
! [B: $i > $o,A: $i] :
( ( B @ one )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(81,plain,
! [B: $i > $o,A: $i] :
( ( B @ one )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[80]) ).
thf(4902,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)],[81]) ).
thf(4943,plain,
! [A: $i] :
( ( A = one )
| ( A != A )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[4902:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).
thf(5018,plain,
! [A: $i] :
( ( A = one )
| ( A != A )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ~ $true ),
inference(lifteq,[status(thm)],[4943]) ).
thf(5210,plain,
! [A: $i] :
( ( A = one )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) ) ),
inference(simp,[status(thm)],[5018]) ).
thf(1,conjecture,
! [A: $i] :
( ( succ @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( succ @ A )
!= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ( succ @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ~ ? [A: $i] :
( ( succ @ A )
= A ),
inference(miniscope,[status(thm)],[6]) ).
thf(8,plain,
( ( succ @ sk1 )
= sk1 ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( succ @ sk1 )
= sk1 ),
inference(lifteq,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( succ @ A )
!= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_is_first) ).
thf(10,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
~ ? [A: $i] :
( ( succ @ A )
= one ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [A: $i] :
( ( succ @ A )
!= one ),
inference(lifteq,[status(thm)],[12]) ).
thf(29,plain,
! [A: $i] :
( ( sk1 != one )
| ( ( succ @ sk1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(30,plain,
sk1 != one,
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 ))]]) ).
thf(9639,plain,
! [A: $i] :
( ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ( one != one )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[5210,30]) ).
thf(9640,plain,
! [A: $i] :
( ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A = one ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[9639]) ).
thf(9641,plain,
( ( sk1
= ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) ) )
!= ( sk1 = one ) ),
inference(pattern_uni,[status(thm)],[9640:[bind(A,$thf( sk1 ))]]) ).
thf(10254,plain,
( ( sk1
= ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) ) )
| ( sk1 = one ) ),
inference(bool_ext,[status(thm)],[9641]) ).
thf(10329,plain,
( ( ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) )
= sk1 )
| ( sk1 = one ) ),
inference(lifteq,[status(thm)],[10254]) ).
thf(10384,plain,
( ( succ
@ ( sk3
@ ^ [A: $i] : ( sk1 != A ) ) )
= sk1 ),
inference(simplifyReflect,[status(thm)],[10329,30]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( succ @ A )
= ( succ @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_injective) ).
thf(14,plain,
! [A: $i,B: $i] :
( ( ( succ @ A )
= ( succ @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( succ @ A )
!= ( succ @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(17,plain,
? [A: $i > $i] :
! [B: $i] :
( ( A @ ( succ @ B ) )
= B ),
inference(detectInverse,[status(thm)],[16]) ).
thf(18,plain,
! [A: $i] :
( ( sk2 @ ( succ @ A ) )
= A ),
inference(cnf,[status(esa)],[17]) ).
thf(31,plain,
! [A: $i] :
( ( sk2 @ ( succ @ A ) )
= A ),
inference(lifteq,[status(thm)],[18]) ).
thf(32,plain,
! [A: $i] :
( ( ( sk2 @ sk1 )
= A )
| ( ( succ @ sk1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,31]) ).
thf(33,plain,
( ( sk2 @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk1 ))]]) ).
thf(151,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( sk2 @ ( succ @ A ) )
!= ( sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[33,31]) ).
thf(153,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( succ @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[151]) ).
thf(10389,plain,
! [A: $i] :
( ( sk1 = A )
| ( sk1 != sk1 )
| ( ( succ
@ ( sk3
@ ^ [B: $i] : ( sk1 != B ) ) )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10384,153]) ).
thf(10390,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( succ
@ ( sk3
@ ^ [B: $i] : ( sk1 != B ) ) )
!= ( succ @ A ) ) ),
inference(simp,[status(thm)],[10389]) ).
thf(10391,plain,
( ( sk3
@ ^ [A: $i] : ( sk1 != A ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[10390:[bind(A,$thf( sk3 @ ^ [B: $i] : ( sk1 != B ) ))]]) ).
thf(21,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ ( sk3 @ A ) )
| ( A @ B ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(10602,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ sk1 )
| ( A @ B )
| ( ( sk3
@ ^ [C: $i] : ( sk1 != C ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10391,21]) ).
thf(10603,plain,
! [A: $i] :
( ~ ( ( sk1 != one ) )
| ( sk1 != sk1 )
| ( sk1 != A ) ),
inference(pattern_uni,[status(thm)],[10602:[bind(A,$thf( ^ [C: $i] : ( sk1 != C ) )),bind(B,$thf( B ))]]) ).
thf(10760,plain,
! [A: $i] :
( ( sk1 = one )
| ( sk1 != sk1 )
| ( sk1 != A ) ),
inference(cnf,[status(esa)],[10603]) ).
thf(10761,plain,
! [A: $i] :
( ( sk1 = one )
| ( sk1 != sk1 )
| ( sk1 != A ) ),
inference(lifteq,[status(thm)],[10760]) ).
thf(10762,plain,
sk1 = one,
inference(simp,[status(thm)],[10761]) ).
thf(10772,plain,
$false,
inference(simplifyReflect,[status(thm)],[10762,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM636^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:00:55 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (182ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 1.85/1.37 % [INFO] eprover registered as external prover.
% 1.85/1.38 % [INFO] Scanning for conjecture ...
% 2.06/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.23/1.50 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.23/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.52 % [INFO] Type checking passed.
% 2.23/1.52 % [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 ...
% 49.24/14.37 % [INFO] Killing All external provers ...
% 49.24/14.38 % Time passed: 14028ms (effective reasoning time: 13382ms)
% 49.24/14.38 % 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)>
% 49.24/14.38 % Axioms used in derivation (3): induction, one_is_first, succ_injective
% 49.24/14.38 % No. of inferences in proof: 51
% 49.24/14.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14028 ms resp. 13382 ms w/o parsing
% 42.27/14.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.27/14.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------