TSTP Solution File: SEU856^5 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU856^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 03:40:18 EDT 2024
% Result : Theorem 8.12s 2.50s
% Output : Refutation 8.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 6 unt; 9 typ; 0 def)
% Number of atoms : 404 ( 107 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 644 ( 171 ~; 167 |; 38 &; 268 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 48 ( 26 ^ 22 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > $o ).
thf(sk2_type,type,
sk2: a > $o ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: a ).
thf(sk6_type,type,
sk6: a ).
thf(sk7_type,type,
sk7: a ).
thf(sk8_type,type,
sk8: a ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM46_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( A = B )
= ( ( ^ [C: a] :
( ( ( B @ C )
& ~ ( A @ C ) )
| ( ( A @ C )
& ~ ( B @ C ) ) ) )
= ( ^ [C: a] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk1 = sk2 )
!= ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) )
!= ( sk1 = sk2 ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(8,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) )
| ( sk1 = sk2 ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
= ( ^ [A: a] : $false ) )
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(17,plain,
! [B: a,A: a] :
( ~ ( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
| ( ( sk2 @ B )
= ( sk1 @ B ) ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(25,plain,
! [B: a,A: a] :
( ( ( sk2 @ B )
= ( sk1 @ B ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(6,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= sk1 )
| ( sk2
!= ( ^ [A: a] : $false ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(11,plain,
( ( ( ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 ) ),
inference(func_ext,[status(esa)],[6]) ).
thf(47,plain,
( ( sk2 @ sk4 )
| ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
| ( sk1 @ sk3 ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(55,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk1 @ sk3 )
| ( sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[47]) ).
thf(59,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[55]) ).
thf(88,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[59]) ).
thf(89,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(7,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 != sk2 ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
( ( ( sk2 @ sk5 )
& ~ ( sk1 @ sk5 ) )
| ( ( sk1 @ sk5 )
& ~ ( sk2 @ sk5 ) )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(13,plain,
( ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk2 @ sk5 )
| ( sk1 @ sk5 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(46,plain,
( ( sk2 @ sk4 )
| ~ ( ( ( sk2 @ sk3 )
& ~ ( sk1 @ sk3 ) )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
| ~ ( sk1 @ sk3 ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(52,plain,
( ~ ( sk1 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(54,plain,
( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[52]) ).
thf(33,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( sk2 @ sk6 )
| ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(183,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[33]) ).
thf(187,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ( sk1 @ sk6 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[183]) ).
thf(90,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[88]) ).
thf(26,plain,
! [B: a,A: a] :
( ( ( sk2 @ B )
= ( sk1 @ B ) )
| ~ ( sk2 @ A )
| ( sk1 @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(506,plain,
! [B: a,A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ B )
= ( sk1 @ B ) )
| ( sk1 @ A )
| ( ( sk2 @ sk3 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[90,26]) ).
thf(507,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ A )
= ( sk1 @ A ) )
| ( sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[506:[bind(A,$thf( sk3 ))]]) ).
thf(598,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ A )
= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[507]) ).
thf(722,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ A )
| ( ( sk2 @ A )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[598,90]) ).
thf(723,plain,
( ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[722:[bind(A,$thf( sk3 ))]]) ).
thf(790,plain,
( ( sk1 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[723]) ).
thf(69,plain,
( ~ ( sk1 @ sk3 )
| ( sk2 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[54]) ).
thf(71,plain,
( ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[69]) ).
thf(822,plain,
( ( sk4 != sk3 )
| ( sk2 @ sk3 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[790,71]) ).
thf(823,plain,
( ( sk4 != sk3 )
| ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[822:[]]) ).
thf(16,plain,
( ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(101,plain,
( ~ ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 )
| ( ( sk2 @ sk5 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[71,16]) ).
thf(109,plain,
( ~ ( sk1 @ sk3 )
| ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[101]) ).
thf(805,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 )
| ( sk5 != sk3 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[790,109]) ).
thf(806,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 )
| ( sk5 != sk3 ) ),
inference(pattern_uni,[status(thm)],[805:[]]) ).
thf(920,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 )
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[790,806]) ).
thf(921,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[920]) ).
thf(928,plain,
( ( sk4 != sk3 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ( sk5 != sk3 ) ),
inference(simp,[status(thm)],[921]) ).
thf(930,plain,
( ( sk4 != sk3 )
| ( sk5 != sk3 )
| ~ ( sk2 @ sk6 )
| ~ ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[928]) ).
thf(28,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( sk2 @ sk6 )
| ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[16]) ).
thf(70,plain,
( ( sk2 @ sk3 )
| ~ ( sk1 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(20,plain,
( ( sk2 = sk1 )
| ( sk1
!= ( ^ [A: a] : $false ) )
| ( sk2
!= ( ^ [A: a] : $false ) )
| ( ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) )
!= ( ^ [A: a] :
( ( ( sk2 @ A )
& ~ ( sk1 @ A ) )
| ( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,6]) ).
thf(21,plain,
( ( sk2 = sk1 )
| ( sk1
!= ( ^ [A: a] : $false ) )
| ( sk2
!= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[20:[]]) ).
thf(32,plain,
( ( sk2 @ sk5 )
| ( sk1 @ sk5 )
| ~ ( sk2 @ sk6 )
| ~ ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(34,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( sk1 @ A ) )
| ( sk1 @ sk7 )
| ( sk2 @ sk8 ) ),
inference(func_ext,[status(esa)],[21]) ).
thf(27,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk2 @ sk6 )
| ~ ( sk1 @ sk6 ) ),
inference(bool_ext,[status(thm)],[16]) ).
thf(48,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( sk1 @ sk6 )
| ( ( ~ ( sk1 @ sk3 )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[28,11]) ).
thf(50,plain,
( ( sk1 @ sk6 )
| ( sk2 @ sk4 )
| ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ( ( ~ ( sk1 @ sk3 )
| ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) ) )
!= ( sk1 @ sk3 ) )
| ( sk6 != sk3 ) ),
inference(simp,[status(thm)],[48]) ).
thf(29,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk5 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(31,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk1 @ sk6 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[29]) ).
thf(812,plain,
( ( sk4 != sk3 )
| ( ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[790,11]) ).
thf(813,plain,
( ( sk4 != sk3 )
| ( ( ( sk1 @ sk3 )
& ~ ( sk2 @ sk3 ) )
!= ( sk1 @ sk3 ) )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[812:[]]) ).
thf(285,plain,
! [B: a,A: a] :
( ( ( sk2 @ B )
= ( sk1 @ B ) )
| ~ ( sk1 @ A )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 )
| ( ( sk2 @ A )
!= ( sk2 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[25,16]) ).
thf(286,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( sk1 @ A ) )
| ~ ( sk1 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( sk5 ))]]) ).
thf(304,plain,
! [A: a] :
( ( ( sk2 @ A )
= ( sk1 @ A ) )
| ~ ( sk1 @ sk5 )
| ( ( sk2 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(30,plain,
( ~ ( sk1 @ sk5 )
| ~ ( sk2 @ sk5 )
| ~ ( sk1 @ sk6 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk5 ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(1074,plain,
$false,
inference(e,[status(thm)],[5,25,89,6,9,13,54,187,3,823,11,928,10,930,28,70,21,33,32,34,59,27,50,16,31,813,304,26,30,790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU856^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 15:46:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.83/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.12/0.89 % [INFO] Parsing done (92ms).
% 1.12/0.90 % [INFO] Running in sequential loop mode.
% 1.50/1.10 % [INFO] eprover registered as external prover.
% 1.50/1.10 % [INFO] cvc4 registered as external prover.
% 1.50/1.10 % [INFO] Scanning for conjecture ...
% 1.50/1.15 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.72/1.17 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.72/1.17 % [INFO] Problem is higher-order (TPTP THF).
% 1.72/1.17 % [INFO] Type checking passed.
% 1.72/1.17 % [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 ...
% 8.12/2.50 % External prover 'e' found a proof!
% 8.12/2.50 % [INFO] Killing All external provers ...
% 8.12/2.50 % Time passed: 1978ms (effective reasoning time: 1598ms)
% 8.12/2.50 % 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)>
% 8.12/2.50 % Axioms used in derivation (0):
% 8.12/2.50 % No. of inferences in proof: 65
% 8.12/2.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1978 ms resp. 1598 ms w/o parsing
% 8.12/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.12/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------