TSTP Solution File: SEU950^5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEU950^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n024.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 : Mon Jun 24 15:29:30 EDT 2024
% Result : Theorem 6.68s 2.67s
% Output : Refutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 90 ( 27 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 188 ( 26 ~; 15 |; 0 &; 141 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 34 ^ 53 !; 6 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(h_type,type,
h: ( $i > $o ) > $i ).
thf(sk1_type,type,
sk1: ( $i > $i > $o ) > $i > $o ).
thf(sk2_type,type,
sk2: $i > $i > $o ).
thf(sk3_type,type,
sk3: $i > ( $i > $i > $o ) > $i ).
thf(1,conjecture,
( ! [A: $i > $o,B: $i > $o] :
( ( ( h @ A )
= ( h @ B ) )
=> ( A = B ) )
=> ? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM573_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $o,B: $i > $o] :
( ( ( h @ A )
= ( h @ B ) )
=> ( A = B ) )
=> ? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o,B: $i > $o] :
( ( ( h @ A )
= ( h @ B ) )
=> ( A = B ) )
=> ? [A: $i > $i > $o] :
! [B: $i > $o] :
? [C: $i] :
( ( A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( h @ A )
!= ( h @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( h @ A )
!= ( h @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
! [A: $i > $o] :
( ( sk2 @ ( h @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(h),[sk2])]) ).
thf(10,plain,
! [B: $i,A: $i > $o] :
( ( sk2 @ ( h @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(4,plain,
! [B: $i,A: $i > $i > $o] :
( ( A @ B )
!= ( sk1 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [B: $i,A: $i > $i > $o] :
( ( A @ B )
!= ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i > $i > $o] :
( ( A @ B )
!= ( sk1 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(11,plain,
! [B: $i,A: $i > $i > $o] :
( ( sk1 @ A @ ( sk3 @ B @ A ) )
!= ( A @ B @ ( sk3 @ B @ A ) ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(14,plain,
! [B: $i,A: $i > $i > $o] :
( ~ ( sk1 @ A @ ( sk3 @ B @ A ) )
| ~ ( A @ B @ ( sk3 @ B @ A ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(15,plain,
! [B: $i,A: $i > $i > $o] :
( ( sk1 @ A @ ( sk3 @ B @ A ) )
| ( A @ B @ ( sk3 @ B @ A ) ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(50,plain,
! [A: $i] :
( ( sk1 @ sk2 @ ( sk3 @ A @ sk2 ) )
| ( sk2 @ A @ ( sk3 @ A @ sk2 ) ) ),
inference(prim_subst,[status(thm)],[15:[bind(A,$thf( sk2 ))]]) ).
thf(62,plain,
! [A: $i] :
( ( sk1 @ sk2 @ ( sk3 @ A @ sk2 ) )
| ( sk2 @ A @ ( sk3 @ A @ sk2 ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(12,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk2 @ ( h @ A ) @ B )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(125,plain,
! [A: $i] :
( ~ ( sk2
@ ( h
@ ^ [B: $i] : $false )
@ A )
| $false ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(133,plain,
! [A: $i] :
~ ( sk2
@ ( h
@ ^ [B: $i] : $false )
@ A ),
inference(simp,[status(thm)],[125]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( sk1 @ sk2 @ ( sk3 @ A @ sk2 ) )
| ( ( sk2 @ A @ ( sk3 @ A @ sk2 ) )
!= ( sk2
@ ( h
@ ^ [C: $i] : $false )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[62,133]) ).
thf(189,plain,
( sk1 @ sk2
@ ( sk3
@ ( h
@ ^ [A: $i] : $false )
@ sk2 ) ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( h @ ^ [C: $i] : $false )),bind(B,$thf( sk3 @ ( h @ ^ [C: $i] : $false ) @ sk2 ))]]) ).
thf(48,plain,
! [A: $i] :
( ( sk1
@ ^ [B: $i,C: $i] : $false
@ ( sk3 @ A
@ ^ [B: $i,C: $i] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[15:[bind(A,$thf( ^ [C: $i] : ^ [D: $i] : $false ))]]) ).
thf(60,plain,
! [A: $i] :
( sk1
@ ^ [B: $i,C: $i] : $false
@ ( sk3 @ A
@ ^ [B: $i,C: $i] : $false ) ),
inference(simp,[status(thm)],[48]) ).
thf(100,plain,
! [D: $i,C: $i > $i > $o,B: $i > $o,A: $i > $o] :
( ( ( h @ A )
!= ( h @ B ) )
| ( B
!= ( C @ D ) )
| ( A
!= ( sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(101,plain,
! [C: $i,B: $i > $i > $o,A: $i > $o] :
( ( ( h @ ( sk1 @ B ) )
!= ( h @ A ) )
| ( A
!= ( B @ C ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk1 @ C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D ))]]) ).
thf(109,plain,
! [B: $i,A: $i > $i > $o] :
( ( h @ ( sk1 @ A ) )
!= ( h @ ( A @ B ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(22,plain,
! [A: $i] :
( ~ ( sk1
@ ^ [B: $i,C: $i] : $true
@ ( sk3 @ A
@ ^ [B: $i,C: $i] : $true ) )
| ~ $true ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [C: $i] : ^ [D: $i] : $true ))]]) ).
thf(34,plain,
! [A: $i] :
~ ( sk1
@ ^ [B: $i,C: $i] : $true
@ ( sk3 @ A
@ ^ [B: $i,C: $i] : $true ) ),
inference(simp,[status(thm)],[22]) ).
thf(72,plain,
! [C: $i,B: $i > $i > $o,A: $i] :
( ~ ( sk1 @ B @ ( sk3 @ C @ B ) )
| ( ( sk1
@ ^ [D: $i,E: $i] : $false
@ ( sk3 @ A
@ ^ [D: $i,E: $i] : $false ) )
!= ( B @ C @ ( sk3 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,14]) ).
thf(76,plain,
! [A: $i] :
~ ( sk1
@ ^ [B: $i,C: $i] :
( sk1
@ ^ [D: $i,E: $i] : $false
@ B )
@ ( sk3
@ ( sk3 @ A
@ ^ [B: $i,C: $i] : $false )
@ ^ [B: $i,C: $i] :
( sk1
@ ^ [D: $i,E: $i] : $false
@ B ) ) ),
inference(pre_uni,[status(thm)],[72:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ^ [E: $i] : ( sk1 @ ^ [F: $i] : ^ [G: $i] : $false @ D ) )),bind(C,$thf( sk3 @ A @ ^ [D: $i] : ^ [E: $i] : $false ))]]) ).
thf(317,plain,
$false,
inference(e,[status(thm)],[10,14,189,133,60,9,109,34,12,3,11,8,76,7,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU950^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 21 17:33:40 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.99 % [INFO] Parsing done (118ms).
% 1.13/1.00 % [INFO] Running in sequential loop mode.
% 1.58/1.22 % [INFO] eprover registered as external prover.
% 1.58/1.22 % [INFO] Scanning for conjecture ...
% 1.72/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.72/1.30 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.72/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.72/1.30 % [INFO] Type checking passed.
% 1.72/1.30 % [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 ...
% 6.68/2.67 % External prover 'e' found a proof!
% 6.68/2.67 % [INFO] Killing All external provers ...
% 6.68/2.67 % Time passed: 2135ms (effective reasoning time: 1659ms)
% 6.68/2.67 % 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)>
% 6.68/2.67 % Axioms used in derivation (0):
% 6.68/2.67 % No. of inferences in proof: 30
% 6.68/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2135 ms resp. 1659 ms w/o parsing
% 6.68/2.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.68/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------