TSTP Solution File: SEU933^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU933^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 21 03:44:17 EDT 2024
% Result : Theorem 77.50s 13.86s
% Output : Refutation 77.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 16 unt; 6 typ; 0 def)
% Number of atoms : 141 ( 78 equ; 8 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 469 ( 93 ~; 79 |; 6 &; 273 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 117 ( 117 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 8 con; 0-4 aty)
% Number of variables : 167 ( 82 ^ 85 !; 0 ?; 167 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $i ).
thf(a_type,type,
a: $i ).
thf(sk1_type,type,
sk1: ( $i > $i ) > ( $i > $i ) > $o ).
thf(sk2_type,type,
sk2: ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ).
thf(sk3_type,type,
sk3: ( ( $i > $i ) > $o ) > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(1,conjecture,
( ( a != b )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
=> ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM196B_pme) ).
thf(2,negated_conjecture,
~ ( ( a != b )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
=> ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( a != b )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
=> ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk2 @ B @ A @ A )
| ( sk1 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ B @ A
@ ^ [C: $i] : ( B @ ( A @ C ) ) )
| ( sk1 @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( sk1 @ A @ B )
| ( sk1 @ C @ D )
| ( ( sk2 @ B @ A @ A )
!= ( sk2 @ D @ C
@ ^ [E: $i] : ( D @ ( C @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[4,9]) ).
thf(20,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk1 @ A @ B )
| ( sk1 @ A @ B )
| ( A
!= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[19:[bind(A,$thf( C )),bind(B,$thf( D ))]]) ).
thf(21,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk1 @ A @ B )
| ( sk1 @ A @ B )
| ( A
!= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[20:[]]) ).
thf(22,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk1 @ A @ B )
| ( A
!= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(24,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( B @ ( A @ ( sk4 @ B @ A ) ) )
!= ( A @ ( sk4 @ B @ A ) ) )
| ( sk1 @ A @ B ) ),
inference(func_ext,[status(esa)],[22]) ).
thf(5,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ~ ( C @ A )
| ~ ( C
@ ^ [D: $i] : ( A @ ( sk3 @ C @ B @ A @ D ) ) )
| ( C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ~ ( C @ A )
| ~ ( C
@ ^ [D: $i] : ( A @ ( sk3 @ C @ B @ A @ D ) ) )
| ( C @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(40,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ~ ( C @ A )
| ( C @ B )
| ( ( C
@ ^ [D: $i] : ( A @ ( sk3 @ C @ B @ A @ D ) ) )
!= ( sk1 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[12]) ).
thf(58,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ( A != A )
| ( A = B )
| ( ( A
= ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
!= ( sk1 @ A @ B ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( (=) @ ( $i > $i ) @ A ))]]) ).
thf(67,plain,
! [B: $i > $i,A: $i > $i] :
( ( A != A )
| ( A = B )
| ~ ( sk1 @ A @ B )
| ( ( A
= ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
!= ( sk1 @ A @ B ) )
| ~ $true ),
inference(lifteq,[status(thm)],[58]) ).
thf(99,plain,
! [B: $i > $i,A: $i > $i] :
( ( A = B )
| ~ ( sk1 @ A @ B )
| ( ( A
= ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
!= ( sk1 @ A @ B ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(8,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ~ ( C @ A )
| ( C @ ( sk3 @ C @ B @ A ) )
| ( C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ( A != A )
| ( A
= ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
| ( A = B ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (@) )),bind(B,$thf( A )),bind(C,$thf( (=) @ ( $i > $i ) @ (@) ))]]) ).
thf(16,plain,
! [B: $i > $i,A: $i > $i] :
( ( A != A )
| ( A
= ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
| ( A = B )
| ~ ( sk1 @ A @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
! [B: $i > $i,A: $i > $i] :
( ( A
= ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
| ( A = B )
| ~ ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[16]) ).
thf(209,plain,
! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( A = B )
| ~ ( sk1 @ A @ B )
| ~ ( sk1 @ C @ D )
| ~ ( E @ C )
| ~ ( E @ A )
| ( E @ D )
| ( ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A )
!= ( ^ [F: $i] : ( C @ ( sk3 @ E @ D @ C @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,12]) ).
thf(253,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( ^ [C: $i] : C )
= A )
| ~ ( sk1
@ ^ [C: $i] : C
@ A )
| ~ ( sk1
@ ^ [C: $i] : C
@ B )
| ( ( ^ [C: $i] : C )
!= ( ^ [C: $i] : C ) )
| ( ( ^ [C: $i] : C )
!= ( ^ [C: $i] : C ) )
| ( ( ^ [C: $i] : C )
= B )
| ( ( ^ [C: $i] : A )
!= ( ^ [C: $i] : B ) ) ),
inference(pre_uni,[status(thm)],[209:[bind(A,$thf( ^ [F: $i] : F )),bind(B,$thf( B )),bind(C,$thf( ^ [F: $i] : F )),bind(D,$thf( D )),bind(E,$thf( (=) @ ( $i > $i ) @ ^ [F: $i] : F ))]]) ).
thf(254,plain,
! [A: $i > $i] :
( ( ( ^ [B: $i] : B )
= A )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ~ ( sk1
@ ^ [B: $i] : B
@ A )
| ~ ( sk1
@ ^ [B: $i] : B
@ A )
| ( ( ^ [B: $i] : B )
= A ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( (@) )),bind(B,$thf( (@) ))]]) ).
thf(281,plain,
! [A: $i > $i] :
( ( ( ^ [B: $i] : B )
= A )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ~ ( sk1
@ ^ [B: $i] : B
@ A )
| ~ ( sk1
@ ^ [B: $i] : B
@ A )
| ( ( ^ [B: $i] : B )
= A ) ),
inference(lifteq,[status(thm)],[254]) ).
thf(282,plain,
! [A: $i > $i] :
( ( ( ^ [B: $i] : B )
= A )
| ~ ( sk1
@ ^ [B: $i] : B
@ A ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
! [B: $i,A: $i > $i] :
( ( ( A @ B )
= B )
| ~ ( sk1
@ ^ [C: $i] : C
@ A ) ),
inference(func_ext,[status(esa)],[282]) ).
thf(7,plain,
a != b,
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
a != b,
inference(lifteq,[status(thm)],[7]) ).
thf(754,plain,
! [B: $i,A: $i > $i] :
( ~ ( sk1
@ ^ [C: $i] : C
@ A )
| ( B != b )
| ( ( A @ B )
!= a ) ),
inference(paramod_ordered,[status(thm)],[283,15]) ).
thf(774,plain,
! [A: $i] :
( ~ ( sk1
@ ^ [B: $i] : B
@ ^ [B: $i] : a )
| ( A != b ) ),
inference(pre_uni,[status(thm)],[754:[bind(A,$thf( ^ [C: $i] : a ))]]) ).
thf(776,plain,
~ ( sk1
@ ^ [A: $i] : A
@ ^ [A: $i] : a ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( b ))]]) ).
thf(796,plain,
! [B: $i > $i,A: $i > $i] :
( ( A
!= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) )
| ( ( sk1 @ A @ B )
!= ( sk1
@ ^ [C: $i] : C
@ ^ [C: $i] : a ) ) ),
inference(paramod_ordered,[status(thm)],[22,776]) ).
thf(797,plain,
( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : a ) ),
inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( ^ [C: $i] : C )),bind(B,$thf( ^ [C: $i] : a ))]]) ).
thf(826,plain,
sk7 != a,
inference(func_ext,[status(esa)],[797]) ).
thf(857,plain,
! [B: $i,A: $i > $i] :
( ~ ( sk1
@ ^ [C: $i] : C
@ A )
| ( B != a )
| ( ( A @ B )
!= sk7 ) ),
inference(paramod_ordered,[status(thm)],[283,826]) ).
thf(858,plain,
! [A: $i] :
( ~ ( sk1
@ ^ [B: $i] : B
@ ^ [B: $i] : sk7 )
| ( A != a ) ),
inference(pre_uni,[status(thm)],[857:[bind(A,$thf( ^ [C: $i] : sk7 ))]]) ).
thf(860,plain,
~ ( sk1
@ ^ [A: $i] : A
@ ^ [A: $i] : sk7 ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( a ))]]) ).
thf(956,plain,
! [B: $i > $i,A: $i > $i] :
( ( A
!= ( ^ [C: $i] : ( B @ ( A @ C ) ) ) )
| ( ( sk1 @ A @ B )
!= ( sk1
@ ^ [C: $i] : C
@ ^ [C: $i] : sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[22,860]) ).
thf(957,plain,
( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : sk7 ) ),
inference(pattern_uni,[status(thm)],[956:[bind(A,$thf( ^ [C: $i] : C )),bind(B,$thf( ^ [C: $i] : sk7 ))]]) ).
thf(4123,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk1 @ A @ B )
| ( ( A
= ( ^ [C: $i] : ( A @ ( sk3 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
!= ( sk1 @ A @ B ) )
| ( B
!= ( ^ [C: $i] : C ) )
| ( A
!= ( ^ [C: $i] : sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[99,957]) ).
thf(4124,plain,
! [A: $i > $i] :
( ~ ( sk1
@ ^ [B: $i] : sk7
@ A )
| ( ( sk1
@ ^ [B: $i] : sk7
@ A )
!= ( ( ^ [B: $i] : sk7 )
= ( ^ [B: $i] : sk7 ) ) )
| ( A
!= ( ^ [B: $i] : B ) ) ),
inference(pattern_uni,[status(thm)],[4123:[bind(A,$thf( ^ [C: $i] : sk7 ))]]) ).
thf(4708,plain,
~ ( sk1
@ ^ [A: $i] : sk7
@ ^ [A: $i] : A ),
inference(simp,[status(thm)],[4124]) ).
thf(5023,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( B @ ( A @ ( sk4 @ B @ A ) ) )
!= ( A @ ( sk4 @ B @ A ) ) )
| ( ( sk1 @ A @ B )
!= ( sk1
@ ^ [C: $i] : sk7
@ ^ [C: $i] : C ) ) ),
inference(paramod_ordered,[status(thm)],[24,4708]) ).
thf(5024,plain,
sk7 != sk7,
inference(pattern_uni,[status(thm)],[5023:[bind(A,$thf( ^ [C: $i] : sk7 )),bind(B,$thf( ^ [C: $i] : C ))]]) ).
thf(5059,plain,
$false,
inference(simp,[status(thm)],[5024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU933^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun May 19 17:05:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.97/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.09 % [INFO] Parsing done (156ms).
% 1.28/1.10 % [INFO] Running in sequential loop mode.
% 1.68/1.44 % [INFO] nitpick registered as external prover.
% 1.83/1.45 % [INFO] Scanning for conjecture ...
% 2.03/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.03/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.03/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.03/1.59 % [INFO] Type checking passed.
% 2.03/1.59 % [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 ...
% 77.50/13.85 % [INFO] Killing All external provers ...
% 77.50/13.86 % Time passed: 13383ms (effective reasoning time: 12751ms)
% 77.50/13.86 % 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)>
% 77.50/13.86 % Axioms used in derivation (0):
% 77.50/13.86 % No. of inferences in proof: 45
% 77.50/13.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 13383 ms resp. 12751 ms w/o parsing
% 77.50/13.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 77.50/13.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------