TSTP Solution File: NUM636^2 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 10:44:57 EDT 2024
% Result : Theorem 42.01s 7.42s
% Output : Refutation 42.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 18 unt; 5 typ; 0 def)
% Number of atoms : 79 ( 75 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 211 ( 67 ~; 42 |; 2 &; 94 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 65 ( 13 ^ 50 !; 2 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(one_type,type,
one: $i ).
thf(succ_type,type,
succ: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: ( $i > $o ) > $i ).
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(18,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(19,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ~ ( A @ ( succ @ ( sk3 @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(38,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ one )
| ~ ~ ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(64,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ( B @ one ) ),
inference(cnf,[status(esa)],[38]) ).
thf(65,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ( B @ one ) ),
inference(simp,[status(thm)],[64]) ).
thf(3532,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B @ one )
| ( ( B
@ ( succ
@ ( sk3
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
!= ( ~ ( B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[65]) ).
thf(3574,plain,
! [A: $i] :
( ( A != A )
| ( A = one )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A != A ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[3532:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).
thf(3607,plain,
! [A: $i] :
( ( A != A )
| ( A = one )
| ( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A != A ) )
| ~ $true ),
inference(lifteq,[status(thm)],[3574]) ).
thf(3761,plain,
! [A: $i] :
( ( A = one )
| ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) ) ),
inference(simp,[status(thm)],[3607]) ).
thf(7159,plain,
! [A: $i] :
( ( A
= ( succ
@ ( sk3
@ ^ [B: $i] : ( A != B ) ) ) )
| ( A = one ) ),
inference(lifteq,[status(thm)],[3761]) ).
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(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] :
( ( sk2 @ ( succ @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(succ),[sk2])]) ).
thf(29,plain,
! [A: $i] :
( ( ( sk2 @ sk1 )
= A )
| ( ( succ @ sk1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(30,plain,
( ( sk2 @ sk1 )
= sk1 ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( sk1 ))]]) ).
thf(138,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( sk2 @ ( succ @ A ) )
!= ( sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[30,17]) ).
thf(140,plain,
! [A: $i] :
( ( sk1 = A )
| ( ( succ @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[138]) ).
thf(7217,plain,
! [B: $i,A: $i] :
( ( A = one )
| ( sk1 = B )
| ( A != sk1 )
| ( ( succ
@ ( sk3
@ ^ [C: $i] : ( A != C ) ) )
!= ( succ @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7159,140]) ).
thf(7218,plain,
! [A: $i] :
( ( A = one )
| ( ( sk3
@ ^ [B: $i] : ( A != B ) )
= sk1 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[7217:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ^ [C: $i] : ( A != C ) ))]]) ).
thf(7480,plain,
( ( sk1 = one )
| ( ( sk3
@ ^ [A: $i] : ( sk1 != A ) )
= sk1 ) ),
inference(simp,[status(thm)],[7218]) ).
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(27,plain,
! [A: $i] :
( ( sk1 != one )
| ( ( succ @ sk1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(28,plain,
sk1 != one,
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk1 ))]]) ).
thf(7540,plain,
( ( sk3
@ ^ [A: $i] : ( sk1 != A ) )
= sk1 ),
inference(simplifyReflect,[status(thm)],[7480,28]) ).
thf(20,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ ( sk3 @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(7562,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ one )
| ( A @ sk1 )
| ( A @ B )
| ( ( sk3
@ ^ [C: $i] : ( sk1 != C ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7540,20]) ).
thf(7563,plain,
! [A: $i] :
( ( sk1 != one )
| ( sk1 != sk1 )
| ( sk1 != A ) ),
inference(pattern_uni,[status(thm)],[7562:[bind(A,$thf( ^ [C: $i] : ( sk1 != C ) )),bind(B,$thf( B ))]]) ).
thf(7655,plain,
! [A: $i] :
( ( sk1 != A )
| ( sk1 != sk1 )
| ( sk1 = one ) ),
inference(cnf,[status(esa)],[7563]) ).
thf(7656,plain,
! [A: $i] :
( ( sk1 != A )
| ( sk1 != sk1 )
| ( sk1 = one ) ),
inference(lifteq,[status(thm)],[7655]) ).
thf(7657,plain,
sk1 = one,
inference(simp,[status(thm)],[7656]) ).
thf(8063,plain,
$false,
inference(simplifyReflect,[status(thm)],[7657,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM636^2 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n023.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 19:27:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/1.02 % [INFO] Parsing done (119ms).
% 1.16/1.03 % [INFO] Running in sequential loop mode.
% 1.60/1.23 % [INFO] nitpick registered as external prover.
% 1.60/1.23 % [INFO] Scanning for conjecture ...
% 1.80/1.28 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.80/1.30 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.80/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.80/1.31 % [INFO] Type checking passed.
% 1.80/1.31 % [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 ...
% 42.01/7.41 % [INFO] Killing All external provers ...
% 42.01/7.41 % Time passed: 6866ms (effective reasoning time: 6379ms)
% 42.01/7.41 % 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)>
% 42.01/7.41 % Axioms used in derivation (3): induction, succ_injective, one_is_first
% 42.01/7.41 % No. of inferences in proof: 44
% 42.01/7.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6866 ms resp. 6379 ms w/o parsing
% 42.01/7.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 42.01/7.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------