TSTP Solution File: SEU895^5 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU895^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 03:44:10 EDT 2024
% Result : Theorem 10.84s 2.90s
% Output : Refutation 10.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 10
% Syntax : Number of formulae : 90 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 281 ( 129 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 520 ( 82 ~; 151 |; 21 &; 266 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 57 ( 8 ^ 28 !; 21 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(f_type,type,
f: b > a ).
thf(y_type,type,
y: b > $o ).
thf(x_type,type,
x: b > $o ).
thf(sk1_type,type,
sk1: a ).
thf(sk2_type,type,
sk2: b ).
thf(sk3_type,type,
sk3: b ).
thf(sk4_type,type,
sk4: b ).
thf(1,conjecture,
( ( ^ [A: a] :
? [B: b] :
( ( ( x @ B )
| ( y @ B ) )
& ( A
= ( f @ B ) ) ) )
= ( ^ [A: a] :
( ? [B: b] :
( ( x @ B )
& ( A
= ( f @ B ) ) )
| ? [B: b] :
( ( y @ B )
& ( A
= ( f @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX5202_pme) ).
thf(2,negated_conjecture,
( ( ^ [A: a] :
? [B: b] :
( ( ( x @ B )
| ( y @ B ) )
& ( A
= ( f @ B ) ) ) )
!= ( ^ [A: a] :
( ? [B: b] :
( ( x @ B )
& ( A
= ( f @ B ) ) )
| ? [B: b] :
( ( y @ B )
& ( A
= ( f @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: a] :
? [B: b] :
( ( ( x @ B )
| ( y @ B ) )
& ( A
= ( f @ B ) ) ) )
!= ( ^ [A: a] :
( ? [B: b] :
( ( x @ B )
& ( A
= ( f @ B ) ) )
| ? [B: b] :
( ( y @ B )
& ( A
= ( f @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: a] :
? [B: b] :
( ( ( x @ B )
| ( y @ B ) )
& ( A
= ( f @ B ) ) ) )
!= ( ^ [A: a] :
( ? [B: b] :
( ( x @ B )
& ( A
= ( f @ B ) ) )
| ? [B: b] :
( ( y @ B )
& ( A
= ( f @ B ) ) ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ? [A: b] :
( ( ( x @ A )
| ( y @ A ) )
& ( sk1
= ( f @ A ) ) ) )
!= ( ? [A: b] :
( ( x @ A )
& ( sk1
= ( f @ A ) ) )
| ? [A: b] :
( ( y @ A )
& ( sk1
= ( f @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(7,plain,
( ? [A: b] :
( ( ( x @ A )
| ( y @ A ) )
& ( sk1
= ( f @ A ) ) )
| ? [A: b] :
( ( x @ A )
& ( sk1
= ( f @ A ) ) )
| ? [A: b] :
( ( y @ A )
& ( sk1
= ( f @ A ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(24,plain,
( ( sk1
= ( f @ sk3 ) )
| ( sk1
= ( f @ sk4 ) )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(31,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk4 )
= sk1 )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(23,plain,
( ( sk1
= ( f @ sk3 ) )
| ( sk1
= ( f @ sk4 ) )
| ( sk1
= ( f @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(29,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk4 )
= sk1 )
| ( ( f @ sk2 )
= sk1 ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(19,plain,
( ( x @ sk3 )
| ( y @ sk4 )
| ( sk1
= ( f @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(30,plain,
( ( ( f @ sk2 )
= sk1 )
| ( x @ sk3 )
| ( y @ sk4 ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(22,plain,
( ( sk1
= ( f @ sk3 ) )
| ( y @ sk4 )
| ( sk1
= ( f @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(27,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk2 )
= sk1 )
| ( y @ sk4 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(6,plain,
( ~ ? [A: b] :
( ( ( x @ A )
| ( y @ A ) )
& ( sk1
= ( f @ A ) ) )
| ~ ( ? [A: b] :
( ( x @ A )
& ( sk1
= ( f @ A ) ) )
| ? [A: b] :
( ( y @ A )
& ( sk1
= ( f @ A ) ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(11,plain,
! [B: b,A: b] :
( ~ ( x @ B )
| ( sk1
!= ( f @ B ) )
| ~ ( x @ A )
| ( sk1
!= ( f @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(17,plain,
! [B: b,A: b] :
( ( ( f @ B )
!= sk1 )
| ( ( f @ A )
!= sk1 )
| ~ ( x @ B )
| ~ ( x @ A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(533,plain,
! [B: b,A: b] :
( ( ( f @ B )
!= sk1 )
| ( ( f @ A )
!= sk1 )
| ~ ( x @ B )
| ( ( x @ A )
!= ( x @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(534,plain,
! [A: b] :
( ( ( f @ A )
!= sk1 )
| ( ( f @ A )
!= sk1 )
| ~ ( x @ A ) ),
inference(pattern_uni,[status(thm)],[533:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(544,plain,
! [A: b] :
( ( ( f @ A )
!= sk1 )
| ~ ( x @ A ) ),
inference(simp,[status(thm)],[534]) ).
thf(593,plain,
! [A: b] :
( ( ( f @ sk2 )
= sk1 )
| ( y @ sk4 )
| ~ ( x @ A )
| ( ( f @ sk3 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27,544]) ).
thf(594,plain,
( ( ( f @ sk2 )
= sk1 )
| ( y @ sk4 )
| ~ ( x @ sk3 ) ),
inference(pattern_uni,[status(thm)],[593:[bind(A,$thf( sk3 ))]]) ).
thf(1783,plain,
( ( ( f @ sk2 )
= sk1 )
| ( y @ sk4 )
| ( ( x @ sk3 )
!= ( x @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[30,594]) ).
thf(1784,plain,
( ( ( f @ sk2 )
= sk1 )
| ( y @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1783:[]]) ).
thf(8,plain,
! [B: b,A: b] :
( ~ ( y @ B )
| ( sk1
!= ( f @ B ) )
| ~ ( y @ A )
| ( sk1
!= ( f @ A ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(12,plain,
! [B: b,A: b] :
( ( ( f @ B )
!= sk1 )
| ( ( f @ A )
!= sk1 )
| ~ ( y @ B )
| ~ ( y @ A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(13,plain,
! [B: b,A: b] :
( ( ( f @ B )
!= sk1 )
| ( ( f @ A )
!= sk1 )
| ~ ( y @ B )
| ~ ( y @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(50,plain,
! [B: b,A: b] :
( ( ( f @ B )
!= sk1 )
| ~ ( y @ B )
| ~ ( y @ A )
| ( ( f @ A )
!= ( f @ B ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[13]) ).
thf(52,plain,
! [A: b] :
( ( ( f @ A )
!= sk1 )
| ~ ( y @ A )
| ~ ( y @ A ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(55,plain,
! [A: b] :
( ( ( f @ A )
!= sk1 )
| ~ ( y @ A ) ),
inference(simp,[status(thm)],[52]) ).
thf(1940,plain,
! [A: b] :
( ( ( f @ sk2 )
= sk1 )
| ( ( f @ A )
!= sk1 )
| ( ( y @ sk4 )
!= ( y @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1784,55]) ).
thf(1941,plain,
( ( ( f @ sk2 )
= sk1 )
| ( ( f @ sk4 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[1940:[bind(A,$thf( sk4 ))]]) ).
thf(2205,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk2 )
= sk1 )
| ( ( f @ sk4 )
!= ( f @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[29,1941]) ).
thf(2206,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk2 )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[2205:[]]) ).
thf(25,plain,
( ( x @ sk3 )
| ( sk1
= ( f @ sk4 ) )
| ( sk1
= ( f @ sk2 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(32,plain,
( ( ( f @ sk4 )
= sk1 )
| ( ( f @ sk2 )
= sk1 )
| ( x @ sk3 ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(203,plain,
! [A: b] :
( ( ( f @ sk2 )
= sk1 )
| ( x @ sk3 )
| ~ ( y @ A )
| ( ( f @ sk4 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32,55]) ).
thf(204,plain,
( ( ( f @ sk2 )
= sk1 )
| ( x @ sk3 )
| ~ ( y @ sk4 ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( sk4 ))]]) ).
thf(1920,plain,
( ( ( f @ sk2 )
= sk1 )
| ( x @ sk3 )
| ( ( y @ sk4 )
!= ( y @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1784,204]) ).
thf(1921,plain,
( ( ( f @ sk2 )
= sk1 )
| ( x @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1920:[]]) ).
thf(2090,plain,
! [A: b] :
( ( ( f @ sk2 )
= sk1 )
| ( ( f @ A )
!= sk1 )
| ( ( x @ sk3 )
!= ( x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1921,544]) ).
thf(2091,plain,
( ( ( f @ sk2 )
= sk1 )
| ( ( f @ sk3 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[2090:[bind(A,$thf( sk3 ))]]) ).
thf(2249,plain,
( ( ( f @ sk2 )
= sk1 )
| ( ( f @ sk3 )
!= ( f @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2206,2091]) ).
thf(2250,plain,
( ( f @ sk2 )
= sk1 ),
inference(pattern_uni,[status(thm)],[2249:[]]) ).
thf(2262,plain,
! [A: b] :
( ~ ( x @ A )
| ( ( f @ sk2 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2250,544]) ).
thf(2263,plain,
~ ( x @ sk2 ),
inference(pattern_uni,[status(thm)],[2262:[bind(A,$thf( sk2 ))]]) ).
thf(2276,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk4 )
= sk1 )
| $false
| ( y @ sk2 ) ),
inference(rewrite,[status(thm)],[31,2263]) ).
thf(2277,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk4 )
= sk1 )
| ( y @ sk2 ) ),
inference(simp,[status(thm)],[2276]) ).
thf(2266,plain,
! [A: b] :
( ~ ( y @ A )
| ( ( f @ sk2 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2250,55]) ).
thf(2267,plain,
~ ( y @ sk2 ),
inference(pattern_uni,[status(thm)],[2266:[bind(A,$thf( sk2 ))]]) ).
thf(2391,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk4 )
= sk1 )
| $false ),
inference(rewrite,[status(thm)],[2277,2267]) ).
thf(2392,plain,
( ( ( f @ sk3 )
= sk1 )
| ( ( f @ sk4 )
= sk1 ) ),
inference(simp,[status(thm)],[2391]) ).
thf(18,plain,
( ( x @ sk3 )
| ( sk1
= ( f @ sk4 ) )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(28,plain,
( ( ( f @ sk4 )
= sk1 )
| ( x @ sk3 )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(2272,plain,
( ( ( f @ sk4 )
= sk1 )
| ( x @ sk3 )
| $false
| ( y @ sk2 ) ),
inference(rewrite,[status(thm)],[28,2263]) ).
thf(2273,plain,
( ( ( f @ sk4 )
= sk1 )
| ( x @ sk3 )
| ( y @ sk2 ) ),
inference(simp,[status(thm)],[2272]) ).
thf(2355,plain,
( ( ( f @ sk4 )
= sk1 )
| ( x @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[2273,2267]) ).
thf(2356,plain,
( ( ( f @ sk4 )
= sk1 )
| ( x @ sk3 ) ),
inference(simp,[status(thm)],[2355]) ).
thf(21,plain,
( ( x @ sk3 )
| ( y @ sk4 )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(2274,plain,
( ( x @ sk3 )
| ( y @ sk4 )
| $false
| ( y @ sk2 ) ),
inference(rewrite,[status(thm)],[21,2263]) ).
thf(2275,plain,
( ( x @ sk3 )
| ( y @ sk4 )
| ( y @ sk2 ) ),
inference(simp,[status(thm)],[2274]) ).
thf(2318,plain,
( ( x @ sk3 )
| ( y @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[2275,2267]) ).
thf(2319,plain,
( ( x @ sk3 )
| ( y @ sk4 ) ),
inference(simp,[status(thm)],[2318]) ).
thf(20,plain,
( ( sk1
= ( f @ sk3 ) )
| ( y @ sk4 )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(26,plain,
( ( ( f @ sk3 )
= sk1 )
| ( y @ sk4 )
| ( x @ sk2 )
| ( y @ sk2 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(1931,plain,
! [A: b] :
( ( y @ sk4 )
| ~ ( x @ A )
| ( ( f @ sk2 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1784,544]) ).
thf(1932,plain,
( ( y @ sk4 )
| ~ ( x @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1931:[bind(A,$thf( sk2 ))]]) ).
thf(1984,plain,
( ( ( f @ sk3 )
= sk1 )
| ( y @ sk4 )
| ( y @ sk2 )
| ( ( x @ sk2 )
!= ( x @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[26,1932]) ).
thf(1985,plain,
( ( ( f @ sk3 )
= sk1 )
| ( y @ sk4 )
| ( y @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1984:[]]) ).
thf(2280,plain,
( ( ( f @ sk3 )
= sk1 )
| ( y @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[1985,2267]) ).
thf(2281,plain,
( ( ( f @ sk3 )
= sk1 )
| ( y @ sk4 ) ),
inference(simp,[status(thm)],[2280]) ).
thf(2283,plain,
! [A: b] :
( ( y @ sk4 )
| ~ ( x @ A )
| ( ( f @ sk3 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2281,544]) ).
thf(2284,plain,
( ( y @ sk4 )
| ~ ( x @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2283:[bind(A,$thf( sk3 ))]]) ).
thf(2320,plain,
( ( y @ sk4 )
| ( ( x @ sk3 )
!= ( x @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2319,2284]) ).
thf(2321,plain,
y @ sk4,
inference(pattern_uni,[status(thm)],[2320:[]]) ).
thf(2329,plain,
! [A: b] :
( ( ( f @ A )
!= sk1 )
| ( ( y @ sk4 )
!= ( y @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2321,55]) ).
thf(2330,plain,
( ( f @ sk4 )
!= sk1 ),
inference(pattern_uni,[status(thm)],[2329:[bind(A,$thf( sk4 ))]]) ).
thf(2357,plain,
x @ sk3,
inference(simplifyReflect,[status(thm)],[2356,2330]) ).
thf(2358,plain,
! [A: b] :
( ( ( f @ A )
!= sk1 )
| ( ( x @ sk3 )
!= ( x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2357,544]) ).
thf(2359,plain,
( ( f @ sk3 )
!= sk1 ),
inference(pattern_uni,[status(thm)],[2358:[bind(A,$thf( sk3 ))]]) ).
thf(2393,plain,
$false,
inference(simplifyReflect,[status(thm)],[2392,2359,2330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU895^5 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.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 : Sun May 19 17:29:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.87/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.90 % [INFO] Parsing done (94ms).
% 1.15/0.90 % [INFO] Running in sequential loop mode.
% 1.48/1.10 % [INFO] nitpick registered as external prover.
% 1.48/1.11 % [INFO] Scanning for conjecture ...
% 1.48/1.16 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.71/1.18 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.71/1.18 % [INFO] Problem is higher-order (TPTP THF).
% 1.71/1.18 % [INFO] Type checking passed.
% 1.71/1.18 % [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 ...
% 10.80/2.87 % [INFO] Killing All external provers ...
% 10.80/2.89 % Time passed: 2343ms (effective reasoning time: 1964ms)
% 10.80/2.89 % 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)>
% 10.84/2.90 % Axioms used in derivation (0):
% 10.84/2.90 % No. of inferences in proof: 81
% 10.84/2.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2343 ms resp. 1964 ms w/o parsing
% 10.90/2.97 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.90/2.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------